Best Known (126, 154, s)-Nets in Base 2
(126, 154, 268)-Net over F2 — Constructive and digital
Digital (126, 154, 268)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (4, 18, 8)-net over F2, using
- net from sequence [i] based on digital (4, 7)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 4 and N(F) ≥ 8, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (4, 7)-sequence over F2, using
- digital (108, 136, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 34, 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, 34, 65)-net over F16, using
- digital (4, 18, 8)-net over F2, using
(126, 154, 682)-Net over F2 — Digital
Digital (126, 154, 682)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2154, 682, F2, 3, 28) (dual of [(682, 3), 1892, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2154, 2046, F2, 28) (dual of [2046, 1892, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2154, 2048, F2, 28) (dual of [2048, 1894, 29]-code), using
- 1 times truncation [i] based on linear OA(2155, 2049, F2, 29) (dual of [2049, 1894, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2155, 2049, F2, 29) (dual of [2049, 1894, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2154, 2048, F2, 28) (dual of [2048, 1894, 29]-code), using
- OOA 3-folding [i] based on linear OA(2154, 2046, F2, 28) (dual of [2046, 1892, 29]-code), using
(126, 154, 12361)-Net in Base 2 — Upper bound on s
There is no (126, 154, 12362)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 22850 769456 448853 318784 347014 888750 922493 137184 > 2154 [i]