Best Known (43−20, 43, s)-Nets in Base 49
(43−20, 43, 344)-Net over F49 — Constructive and digital
Digital (23, 43, 344)-net over F49, using
- t-expansion [i] based on digital (21, 43, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(43−20, 43, 1374)-Net over F49 — Digital
Digital (23, 43, 1374)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4943, 1374, F49, 20) (dual of [1374, 1331, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4943, 2415, F49, 20) (dual of [2415, 2372, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- linear OA(4939, 2401, F49, 20) (dual of [2401, 2362, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(4929, 2401, F49, 15) (dual of [2401, 2372, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(494, 14, F49, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,49)), using
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), using
- Reed–Solomon code RS(45,49) [i]
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4943, 2415, F49, 20) (dual of [2415, 2372, 21]-code), using
(43−20, 43, 1748143)-Net in Base 49 — Upper bound on s
There is no (23, 43, 1748144)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 4 769063 194736 114465 881925 649461 643760 452007 099476 184970 342136 088941 003265 > 4943 [i]