Combinatorial t-designs have nice applications in coding theory, finite geometries and engineering areas. t-designs can be constructed from image sets of a fixed size of some special polynomials. This paper constructs t-designs from the quadratic polynomial \(x^{4}+x^{3}\) over \(\mathrm {GF}(2^{n})\) and determine their parameters. We yield 2-\(\left( 2^n,3\cdot 2^{n-2},3\cdot 2^{n-2}\left( 3\cdot 2^{n-2}-1 \right) \right) \) designs for n even and 3-\(\left( 2^n,2^{n-1},2^{n-1}\left( 2^{n-2}-1 \right) \right) \) designs for n odd.

组合式t设计在编码理论，有限几何和工程领域都有很好的应用。可以从某些特殊多项式的固定大小的图像集构建t设计。本文构建吨-designs从二次多项式\（X ^ {4} + X ^ {3} \）超过\（\ mathrm {GF}（2 ^ {N}）\），并确定它们的参数。我们产生2- \（\ left（2 ^ n，3 \ cdot 2 ^ {n-2}，3 \ cdot 2 ^ {n-2} \ left（3 \ cdot 2 ^ {n-2} -1 \ right）\ right）\）设计n个偶数和3- \（\ left（2 ^ n，2 ^ {n-1}，2 ^ {n-1} \ left（2 ^ {n-2} -1 \ right）\ right）\）设计为n个奇数。