Best Known (25, 51, s)-Nets in Base 9
(25, 51, 82)-Net over F9 — Constructive and digital
Digital (25, 51, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(25,81) in PG(50,9)) for nets [i] based on digital (0, 26, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(25, 51, 84)-Net in Base 9 — Constructive
(25, 51, 84)-net in base 9, using
- base change [i] based on digital (8, 34, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
(25, 51, 110)-Net over F9 — Digital
Digital (25, 51, 110)-net over F9, using
(25, 51, 3917)-Net in Base 9 — Upper bound on s
There is no (25, 51, 3918)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4 641918 123087 951094 951643 615945 553978 059193 034545 > 951 [i]