Best Known (19, 36, s)-Nets in Base 25
(19, 36, 153)-Net over F25 — Constructive and digital
Digital (19, 36, 153)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (10, 27, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- digital (1, 9, 27)-net over F25, using
(19, 36, 482)-Net over F25 — Digital
Digital (19, 36, 482)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2536, 482, F25, 17) (dual of [482, 446, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2536, 637, F25, 17) (dual of [637, 601, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2533, 626, F25, 17) (dual of [626, 593, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2525, 626, F25, 13) (dual of [626, 601, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(253, 11, F25, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2536, 637, F25, 17) (dual of [637, 601, 18]-code), using
(19, 36, 204860)-Net in Base 25 — Upper bound on s
There is no (19, 36, 204861)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 35, 204861)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 8 470493 776533 890514 154690 048795 525200 098282 814145 > 2535 [i]