Best Known (34−19, 34, s)-Nets in Base 25
(34−19, 34, 126)-Net over F25 — Constructive and digital
Digital (15, 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
(34−19, 34, 148)-Net over F25 — Digital
Digital (15, 34, 148)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2534, 148, F25, 19) (dual of [148, 114, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2534, 151, F25, 19) (dual of [151, 117, 20]-code), using
- 20 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 4 times 0, 1, 12 times 0) [i] based on linear OA(2529, 126, F25, 19) (dual of [126, 97, 20]-code), using
- extended algebraic-geometric code AGe(F,106P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- extended algebraic-geometric code AGe(F,106P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- 20 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 4 times 0, 1, 12 times 0) [i] based on linear OA(2529, 126, F25, 19) (dual of [126, 97, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2534, 151, F25, 19) (dual of [151, 117, 20]-code), using
(34−19, 34, 23080)-Net in Base 25 — Upper bound on s
There is no (15, 34, 23081)-net in base 25, because
- 1 times m-reduction [i] would yield (15, 33, 23081)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 13557 215810 955896 264361 422195 446616 782486 550425 > 2533 [i]