Best Known (37−24, 37, s)-Nets in Base 81
(37−24, 37, 224)-Net over F81 — Constructive and digital
Digital (13, 37, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
(37−24, 37, 298)-Net over F81 — Digital
Digital (13, 37, 298)-net over F81, using
- t-expansion [i] based on digital (12, 37, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(37−24, 37, 50666)-Net in Base 81 — Upper bound on s
There is no (13, 37, 50667)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 41117 459128 071273 202029 811702 254925 452309 825375 820678 764945 714248 627521 > 8137 [i]