Best Known (29, 29+27, s)-Nets in Base 25
(29, 29+27, 200)-Net over F25 — Constructive and digital
Digital (29, 56, 200)-net over F25, using
- t-expansion [i] based on digital (25, 56, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
(29, 29+27, 493)-Net over F25 — Digital
Digital (29, 56, 493)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2556, 493, F25, 27) (dual of [493, 437, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2556, 637, F25, 27) (dual of [637, 581, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [i] based on
- linear OA(2553, 626, F25, 27) (dual of [626, 573, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(2545, 626, F25, 23) (dual of [626, 581, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (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([0,13]) ⊂ C([0,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2556, 637, F25, 27) (dual of [637, 581, 28]-code), using
(29, 29+27, 193883)-Net in Base 25 — Upper bound on s
There is no (29, 56, 193884)-net in base 25, because
- 1 times m-reduction [i] would yield (29, 55, 193884)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 77037 456457 274713 549032 813683 658343 097010 358927 788004 815337 453126 908552 539425 > 2555 [i]