Best Known (26, 50, s)-Nets in Base 49
(26, 50, 344)-Net over F49 — Constructive and digital
Digital (26, 50, 344)-net over F49, using
- t-expansion [i] based on digital (21, 50, 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
(26, 50, 1206)-Net over F49 — Digital
Digital (26, 50, 1206)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4950, 1206, F49, 2, 24) (dual of [(1206, 2), 2362, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4950, 2412, F49, 24) (dual of [2412, 2362, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- linear OA(4947, 2401, F49, 24) (dual of [2401, 2354, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- 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(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(23) ⊂ Ce(19) [i] based on
- OOA 2-folding [i] based on linear OA(4950, 2412, F49, 24) (dual of [2412, 2362, 25]-code), using
(26, 50, 1215071)-Net in Base 49 — Upper bound on s
There is no (26, 50, 1215072)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 3 234496 639092 941677 203425 341686 296716 465000 233465 428777 065050 300445 138007 792656 103425 > 4950 [i]