Best Known (171, 171+32, s)-Nets in Base 2
(171, 171+32, 490)-Net over F2 — Constructive and digital
Digital (171, 203, 490)-net over F2, using
- 2 times m-reduction [i] based on digital (171, 205, 490)-net over F2, using
- trace code for nets [i] based on digital (7, 41, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- trace code for nets [i] based on digital (7, 41, 98)-net over F32, using
(171, 171+32, 1382)-Net over F2 — Digital
Digital (171, 203, 1382)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2203, 1382, F2, 2, 32) (dual of [(1382, 2), 2561, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2203, 2065, F2, 2, 32) (dual of [(2065, 2), 3927, 33]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2202, 2065, F2, 2, 32) (dual of [(2065, 2), 3928, 33]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2198, 2063, F2, 2, 32) (dual of [(2063, 2), 3928, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2198, 4126, F2, 32) (dual of [4126, 3928, 33]-code), using
- 1 times truncation [i] based on linear OA(2199, 4127, F2, 33) (dual of [4127, 3928, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2193, 4097, F2, 33) (dual of [4097, 3904, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2169, 4097, F2, 29) (dual of [4097, 3928, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on 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([0,16]) ⊂ C([0,14]) [i] based on
- 1 times truncation [i] based on linear OA(2199, 4127, F2, 33) (dual of [4127, 3928, 34]-code), using
- OOA 2-folding [i] based on linear OA(2198, 4126, F2, 32) (dual of [4126, 3928, 33]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2198, 2063, F2, 2, 32) (dual of [(2063, 2), 3928, 33]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2202, 2065, F2, 2, 32) (dual of [(2065, 2), 3928, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2203, 2065, F2, 2, 32) (dual of [(2065, 2), 3927, 33]-NRT-code), using
(171, 171+32, 44836)-Net in Base 2 — Upper bound on s
There is no (171, 203, 44837)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 12 858943 777809 896294 568657 128773 776041 310072 573373 212273 480894 > 2203 [i]