Best Known (25, 46, s)-Nets in Base 49
(25, 46, 344)-Net over F49 — Constructive and digital
Digital (25, 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
(25, 46, 1655)-Net over F49 — Digital
Digital (25, 46, 1655)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4946, 1655, F49, 21) (dual of [1655, 1609, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4946, 2419, F49, 21) (dual of [2419, 2373, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- linear OA(4941, 2402, F49, 21) (dual of [2402, 2361, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(4929, 2402, F49, 15) (dual of [2402, 2373, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(495, 17, F49, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,49)), using
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- Reed–Solomon code RS(44,49) [i]
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4946, 2419, F49, 21) (dual of [2419, 2373, 22]-code), using
(25, 46, 3807298)-Net in Base 49 — Upper bound on s
There is no (25, 46, 3807299)-net in base 49, because
- 1 times m-reduction [i] would yield (25, 45, 3807299)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 11450 502851 140941 949455 724544 733721 503165 642043 658214 373235 033692 746665 450401 > 4945 [i]