Best Known (131, 131+34, s)-Nets in Base 2
(131, 131+34, 260)-Net over F2 — Constructive and digital
Digital (131, 165, 260)-net over F2, using
- 21 times duplication [i] based on digital (130, 164, 260)-net over F2, using
- t-expansion [i] based on digital (129, 164, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 41, 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, 41, 65)-net over F16, using
- t-expansion [i] based on digital (129, 164, 260)-net over F2, using
(131, 131+34, 432)-Net over F2 — Digital
Digital (131, 165, 432)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2165, 432, F2, 2, 34) (dual of [(432, 2), 699, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2165, 511, F2, 2, 34) (dual of [(511, 2), 857, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2165, 1022, F2, 34) (dual of [1022, 857, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using
- the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using
- OOA 2-folding [i] based on linear OA(2165, 1022, F2, 34) (dual of [1022, 857, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(2165, 511, F2, 2, 34) (dual of [(511, 2), 857, 35]-NRT-code), using
(131, 131+34, 5968)-Net in Base 2 — Upper bound on s
There is no (131, 165, 5969)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 46 779741 699277 499551 985283 810701 137744 878226 074202 > 2165 [i]