Best Known (34−18, 34, s)-Nets in Base 25
(34−18, 34, 126)-Net over F25 — Constructive and digital
Digital (16, 34, 126)-net over F25, using
- t-expansion [i] based on digital (10, 34, 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
(34−18, 34, 210)-Net over F25 — Digital
Digital (16, 34, 210)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2534, 210, F25, 18) (dual of [210, 176, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2534, 312, F25, 18) (dual of [312, 278, 19]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2534, 312, F25, 18) (dual of [312, 278, 19]-code), using
(34−18, 34, 33005)-Net in Base 25 — Upper bound on s
There is no (16, 34, 33006)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 338838 106943 126610 361780 102798 632967 463968 092625 > 2534 [i]