Best Known (185, 185+32, s)-Nets in Base 2
(185, 185+32, 624)-Net over F2 — Constructive and digital
Digital (185, 217, 624)-net over F2, using
- 21 times duplication [i] based on digital (184, 216, 624)-net over F2, using
- t-expansion [i] based on digital (183, 216, 624)-net over F2, using
- trace code for nets [i] based on digital (3, 36, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 36, 104)-net over F64, using
- t-expansion [i] based on digital (183, 216, 624)-net over F2, using
(185, 185+32, 2217)-Net over F2 — Digital
Digital (185, 217, 2217)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2217, 2217, F2, 3, 32) (dual of [(2217, 3), 6434, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2217, 2742, F2, 3, 32) (dual of [(2742, 3), 8009, 33]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2216, 2742, F2, 3, 32) (dual of [(2742, 3), 8010, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2216, 8226, F2, 32) (dual of [8226, 8010, 33]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2214, 8224, F2, 32) (dual of [8224, 8010, 33]-code), using
- 1 times truncation [i] based on linear OA(2215, 8225, F2, 33) (dual of [8225, 8010, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [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]
- linear OA(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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([0,16]) ⊂ C([0,14]) [i] based on
- 1 times truncation [i] based on linear OA(2215, 8225, F2, 33) (dual of [8225, 8010, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2214, 8224, F2, 32) (dual of [8224, 8010, 33]-code), using
- OOA 3-folding [i] based on linear OA(2216, 8226, F2, 32) (dual of [8226, 8010, 33]-code), using
- 21 times duplication [i] based on linear OOA(2216, 2742, F2, 3, 32) (dual of [(2742, 3), 8010, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2217, 2742, F2, 3, 32) (dual of [(2742, 3), 8009, 33]-NRT-code), using
(185, 185+32, 82249)-Net in Base 2 — Upper bound on s
There is no (185, 217, 82250)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 210639 452645 623742 927504 900491 930286 058047 393509 849941 885495 548676 > 2217 [i]