Best Known (13, 13+16, s)-Nets in Base 25
(13, 13+16, 126)-Net over F25 — Constructive and digital
Digital (13, 29, 126)-net over F25, using
- t-expansion [i] based on digital (10, 29, 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
(13, 13+16, 152)-Net over F25 — Digital
Digital (13, 29, 152)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2529, 152, F25, 16) (dual of [152, 123, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2529, 156, F25, 16) (dual of [156, 127, 17]-code), using
(13, 13+16, 18319)-Net in Base 25 — Upper bound on s
There is no (13, 29, 18320)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 34697 647774 611258 094434 688563 873495 376897 > 2529 [i]