Best Known (118, 146, s)-Nets in Base 2
(118, 146, 260)-Net over F2 — Constructive and digital
Digital (118, 146, 260)-net over F2, using
- t-expansion [i] based on digital (117, 146, 260)-net over F2, using
- 2 times m-reduction [i] based on digital (117, 148, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 37, 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, 37, 65)-net over F16, using
- 2 times m-reduction [i] based on digital (117, 148, 260)-net over F2, using
(118, 146, 516)-Net over F2 — Digital
Digital (118, 146, 516)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2146, 516, F2, 2, 28) (dual of [(516, 2), 886, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2146, 525, F2, 2, 28) (dual of [(525, 2), 904, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2146, 1050, F2, 28) (dual of [1050, 904, 29]-code), using
- 1 times truncation [i] based on linear OA(2147, 1051, F2, 29) (dual of [1051, 904, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- 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(2121, 1025, F2, 25) (dual of [1025, 904, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 220−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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([0,14]) ⊂ C([0,12]) [i] based on
- 1 times truncation [i] based on linear OA(2147, 1051, F2, 29) (dual of [1051, 904, 30]-code), using
- OOA 2-folding [i] based on linear OA(2146, 1050, F2, 28) (dual of [1050, 904, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(2146, 525, F2, 2, 28) (dual of [(525, 2), 904, 29]-NRT-code), using
(118, 146, 8311)-Net in Base 2 — Upper bound on s
There is no (118, 146, 8312)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 89 213285 561307 503644 024588 151038 908043 285194 > 2146 [i]