Best Known (30−16, 30, s)-Nets in Base 25
(30−16, 30, 126)-Net over F25 — Constructive and digital
Digital (14, 30, 126)-net over F25, using
- t-expansion [i] based on digital (10, 30, 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
(30−16, 30, 192)-Net over F25 — Digital
Digital (14, 30, 192)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2530, 192, F25, 16) (dual of [192, 162, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2530, 312, F25, 16) (dual of [312, 282, 17]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2530, 312, F25, 16) (dual of [312, 282, 17]-code), using
(30−16, 30, 27396)-Net in Base 25 — Upper bound on s
There is no (14, 30, 27397)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 867520 130435 194689 573366 478603 743000 732865 > 2530 [i]