Best Known (176−20, 176, s)-Nets in Base 2
(176−20, 176, 13110)-Net over F2 — Constructive and digital
Digital (156, 176, 13110)-net over F2, using
- net defined by OOA [i] based on linear OOA(2176, 13110, F2, 20, 20) (dual of [(13110, 20), 262024, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2176, 131100, F2, 20) (dual of [131100, 130924, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2176, 131104, F2, 20) (dual of [131104, 130928, 21]-code), using
- 1 times truncation [i] based on linear OA(2177, 131105, F2, 21) (dual of [131105, 130928, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2171, 131073, F2, 21) (dual of [131073, 130902, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2137, 131073, F2, 17) (dual of [131073, 130936, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- 1 times truncation [i] based on linear OA(2177, 131105, F2, 21) (dual of [131105, 130928, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2176, 131104, F2, 20) (dual of [131104, 130928, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2176, 131100, F2, 20) (dual of [131100, 130924, 21]-code), using
(176−20, 176, 26220)-Net over F2 — Digital
Digital (156, 176, 26220)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2176, 26220, F2, 5, 20) (dual of [(26220, 5), 130924, 21]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2176, 131100, F2, 20) (dual of [131100, 130924, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2176, 131104, F2, 20) (dual of [131104, 130928, 21]-code), using
- 1 times truncation [i] based on linear OA(2177, 131105, F2, 21) (dual of [131105, 130928, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2171, 131073, F2, 21) (dual of [131073, 130902, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2137, 131073, F2, 17) (dual of [131073, 130936, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- 1 times truncation [i] based on linear OA(2177, 131105, F2, 21) (dual of [131105, 130928, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2176, 131104, F2, 20) (dual of [131104, 130928, 21]-code), using
- OOA 5-folding [i] based on linear OA(2176, 131100, F2, 20) (dual of [131100, 130924, 21]-code), using
(176−20, 176, 899698)-Net in Base 2 — Upper bound on s
There is no (156, 176, 899699)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 95780 993348 530417 270475 537227 695344 862378 691059 863466 > 2176 [i]