Best Known (46−22, 46, s)-Nets in Base 49
(46−22, 46, 344)-Net over F49 — Constructive and digital
Digital (24, 46, 344)-net over F49, using
- t-expansion [i] based on digital (21, 46, 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
(46−22, 46, 1206)-Net over F49 — Digital
Digital (24, 46, 1206)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4946, 1206, F49, 2, 22) (dual of [(1206, 2), 2366, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4946, 2412, F49, 22) (dual of [2412, 2366, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(4943, 2401, F49, 22) (dual of [2401, 2358, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4935, 2401, F49, 18) (dual of [2401, 2366, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(493, 11, F49, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,49) or 11-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(4946, 2412, F49, 22) (dual of [2412, 2366, 23]-code), using
(46−22, 46, 1196365)-Net in Base 49 — Upper bound on s
There is no (24, 46, 1196366)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 561078 280505 419202 998642 271414 905602 999467 066988 878858 085903 283125 360985 020385 > 4946 [i]