Best Known (132−24, 132, s)-Nets in Base 2
(132−24, 132, 263)-Net over F2 — Constructive and digital
Digital (108, 132, 263)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 3)-net over F2, using
- net from sequence [i] based on digital (0, 2)-sequence over F2, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 0 and N(F) ≥ 3, using
- the rational function field F2(x) [i]
- Niederreiter sequence [i]
- Sobol sequence [i]
- net from sequence [i] based on digital (0, 2)-sequence over F2, using
- digital (96, 120, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 30, 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, 30, 65)-net over F16, using
- digital (0, 12, 3)-net over F2, using
(132−24, 132, 682)-Net over F2 — Digital
Digital (108, 132, 682)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2132, 682, F2, 3, 24) (dual of [(682, 3), 1914, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2132, 2046, F2, 24) (dual of [2046, 1914, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2132, 2048, F2, 24) (dual of [2048, 1916, 25]-code), using
- 1 times truncation [i] based on linear OA(2133, 2049, F2, 25) (dual of [2049, 1916, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2133, 2049, F2, 25) (dual of [2049, 1916, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2132, 2048, F2, 24) (dual of [2048, 1916, 25]-code), using
- OOA 3-folding [i] based on linear OA(2132, 2046, F2, 24) (dual of [2046, 1914, 25]-code), using
(132−24, 132, 10814)-Net in Base 2 — Upper bound on s
There is no (108, 132, 10815)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 5450 060040 128817 824765 501153 695252 439853 > 2132 [i]