Best Known (49−24, 49, s)-Nets in Base 49
(49−24, 49, 344)-Net over F49 — Constructive and digital
Digital (25, 49, 344)-net over F49, using
- t-expansion [i] based on digital (21, 49, 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
(49−24, 49, 1087)-Net over F49 — Digital
Digital (25, 49, 1087)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4949, 1087, F49, 2, 24) (dual of [(1087, 2), 2125, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4949, 1204, F49, 2, 24) (dual of [(1204, 2), 2359, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4949, 2408, F49, 24) (dual of [2408, 2359, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4949, 2409, F49, 24) (dual of [2409, 2360, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [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(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(492, 8, F49, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4949, 2409, F49, 24) (dual of [2409, 2360, 25]-code), using
- OOA 2-folding [i] based on linear OA(4949, 2408, F49, 24) (dual of [2408, 2359, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(4949, 1204, F49, 2, 24) (dual of [(1204, 2), 2359, 25]-NRT-code), using
(49−24, 49, 878519)-Net in Base 49 — Upper bound on s
There is no (25, 49, 878520)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 66010 318629 065016 419300 723358 871485 088807 417121 837331 379289 951007 916755 945827 341825 > 4949 [i]