Best Known (37−23, 37, s)-Nets in Base 81
(37−23, 37, 224)-Net over F81 — Constructive and digital
Digital (14, 37, 224)-net over F81, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(37−23, 37, 298)-Net over F81 — Digital
Digital (14, 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
(37−23, 37, 108107)-Net in Base 81 — Upper bound on s
There is no (14, 37, 108108)-net in base 81, because
- 1 times m-reduction [i] would yield (14, 36, 108108)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 507 571603 768190 313532 324711 907587 246216 512656 194094 793111 300227 807041 > 8136 [i]