Best Known (176−32, 176, s)-Nets in Base 2
(176−32, 176, 320)-Net over F2 — Constructive and digital
Digital (144, 176, 320)-net over F2, using
- 21 times duplication [i] based on digital (143, 175, 320)-net over F2, using
- trace code for nets [i] based on digital (3, 35, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- trace code for nets [i] based on digital (3, 35, 64)-net over F32, using
(176−32, 176, 706)-Net over F2 — Digital
Digital (144, 176, 706)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2176, 706, F2, 2, 32) (dual of [(706, 2), 1236, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2176, 1024, F2, 2, 32) (dual of [(1024, 2), 1872, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2176, 2048, F2, 32) (dual of [2048, 1872, 33]-code), using
- 1 times truncation [i] based on linear OA(2177, 2049, F2, 33) (dual of [2049, 1872, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2177, 2049, F2, 33) (dual of [2049, 1872, 34]-code), using
- OOA 2-folding [i] based on linear OA(2176, 2048, F2, 32) (dual of [2048, 1872, 33]-code), using
- discarding factors / shortening the dual code based on linear OOA(2176, 1024, F2, 2, 32) (dual of [(1024, 2), 1872, 33]-NRT-code), using
(176−32, 176, 13903)-Net in Base 2 — Upper bound on s
There is no (144, 176, 13904)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 95794 838785 060387 464386 717689 441061 447822 299199 613060 > 2176 [i]