Best Known (134, 134+32, s)-Nets in Base 2
(134, 134+32, 260)-Net over F2 — Constructive and digital
Digital (134, 166, 260)-net over F2, using
- t-expansion [i] based on digital (132, 166, 260)-net over F2, using
- 2 times m-reduction [i] based on digital (132, 168, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 42, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 42, 65)-net over F16, using
- 2 times m-reduction [i] based on digital (132, 168, 260)-net over F2, using
(134, 134+32, 525)-Net over F2 — Digital
Digital (134, 166, 525)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2166, 525, F2, 2, 32) (dual of [(525, 2), 884, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2166, 1050, F2, 32) (dual of [1050, 884, 33]-code), using
- 1 times truncation [i] based on linear OA(2167, 1051, F2, 33) (dual of [1051, 884, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2161, 1025, F2, 33) (dual of [1025, 864, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 220−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2141, 1025, F2, 29) (dual of [1025, 884, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 220−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-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(2167, 1051, F2, 33) (dual of [1051, 884, 34]-code), using
- OOA 2-folding [i] based on linear OA(2166, 1050, F2, 32) (dual of [1050, 884, 33]-code), using
(134, 134+32, 9007)-Net in Base 2 — Upper bound on s
There is no (134, 166, 9008)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 93 652045 488914 267076 952462 006370 465706 633535 232250 > 2166 [i]