Best Known (126, 126+24, s)-Nets in Base 2
(126, 126+24, 480)-Net over F2 — Constructive and digital
Digital (126, 150, 480)-net over F2, using
- trace code for nets [i] based on digital (1, 25, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(126, 126+24, 1326)-Net over F2 — Digital
Digital (126, 150, 1326)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2150, 1326, F2, 3, 24) (dual of [(1326, 3), 3828, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2150, 1375, F2, 3, 24) (dual of [(1375, 3), 3975, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2150, 4125, F2, 24) (dual of [4125, 3975, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2150, 4126, F2, 24) (dual of [4126, 3976, 25]-code), using
- 1 times truncation [i] based on linear OA(2151, 4127, F2, 25) (dual of [4127, 3976, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2145, 4097, F2, 25) (dual of [4097, 3952, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2121, 4097, F2, 21) (dual of [4097, 3976, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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([0,12]) ⊂ C([0,10]) [i] based on
- 1 times truncation [i] based on linear OA(2151, 4127, F2, 25) (dual of [4127, 3976, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2150, 4126, F2, 24) (dual of [4126, 3976, 25]-code), using
- OOA 3-folding [i] based on linear OA(2150, 4125, F2, 24) (dual of [4125, 3975, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(2150, 1375, F2, 3, 24) (dual of [(1375, 3), 3975, 25]-NRT-code), using
(126, 126+24, 30618)-Net in Base 2 — Upper bound on s
There is no (126, 150, 30619)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1427 355179 733761 388764 665355 882905 712415 623116 > 2150 [i]