Best Known (15, 15+70, s)-Nets in Base 25
(15, 15+70, 126)-Net over F25 — Constructive and digital
Digital (15, 85, 126)-net over F25, using
- t-expansion [i] based on digital (10, 85, 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
(15, 15+70, 140)-Net over F25 — Digital
Digital (15, 85, 140)-net over F25, using
- net from sequence [i] based on digital (15, 139)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 15 and N(F) ≥ 140, using
(15, 15+70, 1420)-Net in Base 25 — Upper bound on s
There is no (15, 85, 1421)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 67540 954097 934756 461191 351367 921541 683339 892796 234270 084087 611635 195750 051279 891749 980478 939953 323248 878552 537545 663209 > 2585 [i]