Best Known (26, 47, s)-Nets in Base 49
(26, 47, 344)-Net over F49 — Constructive and digital
Digital (26, 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
(26, 47, 2033)-Net over F49 — Digital
Digital (26, 47, 2033)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4947, 2033, F49, 21) (dual of [2033, 1986, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4947, 2421, F49, 21) (dual of [2421, 2374, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(4941, 2401, F49, 21) (dual of [2401, 2360, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4927, 2401, F49, 14) (dual of [2401, 2374, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(496, 20, F49, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,49)), using
- discarding factors / shortening the dual code based on linear OA(496, 49, F49, 6) (dual of [49, 43, 7]-code or 49-arc in PG(5,49)), using
- Reed–Solomon code RS(43,49) [i]
- discarding factors / shortening the dual code based on linear OA(496, 49, F49, 6) (dual of [49, 43, 7]-code or 49-arc in PG(5,49)), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4947, 2421, F49, 21) (dual of [2421, 2374, 22]-code), using
(26, 47, 5618710)-Net in Base 49 — Upper bound on s
There is no (26, 47, 5618711)-net in base 49, because
- 1 times m-reduction [i] would yield (26, 46, 5618711)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 561073 718551 767837 006836 848824 914682 149276 510981 446419 294325 376011 401282 277153 > 4946 [i]