Best Known (208−32, 208, s)-Nets in Base 2
(208−32, 208, 520)-Net over F2 — Constructive and digital
Digital (176, 208, 520)-net over F2, using
- 23 times duplication [i] based on digital (173, 205, 520)-net over F2, using
- trace code for nets [i] based on digital (9, 41, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- trace code for nets [i] based on digital (9, 41, 104)-net over F32, using
(208−32, 208, 2016)-Net over F2 — Digital
Digital (176, 208, 2016)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2208, 2016, F2, 4, 32) (dual of [(2016, 4), 7856, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2208, 2048, F2, 4, 32) (dual of [(2048, 4), 7984, 33]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2208, 8192, F2, 32) (dual of [8192, 7984, 33]-code), using
- 1 times truncation [i] based on linear OA(2209, 8193, F2, 33) (dual of [8193, 7984, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, 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(2209, 8193, F2, 33) (dual of [8193, 7984, 34]-code), using
- OOA 4-folding [i] based on linear OA(2208, 8192, F2, 32) (dual of [8192, 7984, 33]-code), using
- discarding factors / shortening the dual code based on linear OOA(2208, 2048, F2, 4, 32) (dual of [(2048, 4), 7984, 33]-NRT-code), using
(208−32, 208, 55685)-Net in Base 2 — Upper bound on s
There is no (176, 208, 55686)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 411 384585 995741 160010 187586 176554 899070 957747 511856 352184 187336 > 2208 [i]