Best Known (12, 12+16, s)-Nets in Base 25
(12, 12+16, 126)-Net over F25 — Constructive and digital
Digital (12, 28, 126)-net over F25, using
- t-expansion [i] based on digital (10, 28, 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
(12, 12+16, 127)-Net over F25 — Digital
Digital (12, 28, 127)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2528, 127, F25, 2, 16) (dual of [(127, 2), 226, 17]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2526, 126, F25, 2, 16) (dual of [(126, 2), 226, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,235P) [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 NRT-code AGe(2;F,235P) [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2526, 126, F25, 2, 16) (dual of [(126, 2), 226, 17]-NRT-code), using
(12, 12+16, 12249)-Net in Base 25 — Upper bound on s
There is no (12, 28, 12250)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 1387 858131 626620 184499 185317 919558 812801 > 2528 [i]