Best Known (17, 17+15, s)-Nets in Base 25
(17, 17+15, 152)-Net over F25 — Constructive and digital
Digital (17, 32, 152)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (10, 25, 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 (0, 7, 26)-net over F25, using
(17, 17+15, 503)-Net over F25 — Digital
Digital (17, 32, 503)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2532, 503, F25, 15) (dual of [503, 471, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2532, 637, F25, 15) (dual of [637, 605, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- linear OA(2529, 626, F25, 15) (dual of [626, 597, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(2521, 626, F25, 11) (dual of [626, 605, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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([0,7]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2532, 637, F25, 15) (dual of [637, 605, 16]-code), using
(17, 17+15, 218563)-Net in Base 25 — Upper bound on s
There is no (17, 32, 218564)-net in base 25, because
- 1 times m-reduction [i] would yield (17, 31, 218564)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 21 684247 277682 332024 043959 415547 375757 783329 > 2531 [i]