Best Known (47−22, 47, s)-Nets in Base 49
(47−22, 47, 344)-Net over F49 — Constructive and digital
Digital (25, 47, 344)-net over F49, using
- t-expansion [i] based on digital (21, 47, 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
(47−22, 47, 1326)-Net over F49 — Digital
Digital (25, 47, 1326)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4947, 1326, F49, 22) (dual of [1326, 1279, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4947, 2415, F49, 22) (dual of [2415, 2368, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [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(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(4947, 2415, F49, 22) (dual of [2415, 2368, 23]-code), using
(47−22, 47, 1704191)-Net in Base 49 — Upper bound on s
There is no (25, 47, 1704192)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 27 492630 582445 232246 831466 550756 208086 370469 919569 240885 111132 046698 772804 767745 > 4947 [i]