Best Known (15, 32, s)-Nets in Base 25
(15, 32, 126)-Net over F25 — Constructive and digital
Digital (15, 32, 126)-net over F25, using
- t-expansion [i] based on digital (10, 32, 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
(15, 32, 201)-Net over F25 — Digital
Digital (15, 32, 201)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2532, 201, F25, 17) (dual of [201, 169, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2532, 312, F25, 17) (dual of [312, 280, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(2532, 312, F25, 17) (dual of [312, 280, 18]-code), using
(15, 32, 40969)-Net in Base 25 — Upper bound on s
There is no (15, 32, 40970)-net in base 25, because
- 1 times m-reduction [i] would yield (15, 31, 40970)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 21 688133 344281 966043 840636 909550 922655 756417 > 2531 [i]