Best Known (86−72, 86, s)-Nets in Base 25
(86−72, 86, 126)-Net over F25 — Constructive and digital
Digital (14, 86, 126)-net over F25, using
- t-expansion [i] based on digital (10, 86, 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
(86−72, 86, 130)-Net over F25 — Digital
Digital (14, 86, 130)-net over F25, using
- net from sequence [i] based on digital (14, 129)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 14 and N(F) ≥ 130, using
(86−72, 86, 1281)-Net in Base 25 — Upper bound on s
There is no (14, 86, 1282)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 1 699431 005676 449329 833905 987198 379785 474233 566351 611175 186356 576937 946085 422553 574231 238860 544007 582524 023530 461858 722625 > 2586 [i]