Best Known (102, 126, s)-Nets in Base 2
(102, 126, 260)-Net over F2 — Constructive and digital
Digital (102, 126, 260)-net over F2, using
- 2 times m-reduction [i] based on digital (102, 128, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 32, 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, 32, 65)-net over F16, using
(102, 126, 490)-Net over F2 — Digital
Digital (102, 126, 490)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2126, 490, F2, 2, 24) (dual of [(490, 2), 854, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2126, 525, F2, 2, 24) (dual of [(525, 2), 924, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2126, 1050, F2, 24) (dual of [1050, 924, 25]-code), using
- 1 times truncation [i] based on linear OA(2127, 1051, F2, 25) (dual of [1051, 924, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- 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(2101, 1025, F2, 21) (dual of [1025, 924, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 220−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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([0,12]) ⊂ C([0,10]) [i] based on
- 1 times truncation [i] based on linear OA(2127, 1051, F2, 25) (dual of [1051, 924, 26]-code), using
- OOA 2-folding [i] based on linear OA(2126, 1050, F2, 24) (dual of [1050, 924, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(2126, 525, F2, 2, 24) (dual of [(525, 2), 924, 25]-NRT-code), using
(102, 126, 7641)-Net in Base 2 — Upper bound on s
There is no (102, 126, 7642)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 85 124748 580017 749907 946577 001326 407372 > 2126 [i]