Best Known (9, 57, s)-Nets in Base 81
(9, 57, 172)-Net over F81 — Constructive and digital
Digital (9, 57, 172)-net over F81, using
- t-expansion [i] based on digital (7, 57, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(9, 57, 244)-Net over F81 — Digital
Digital (9, 57, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
(9, 57, 4165)-Net in Base 81 — Upper bound on s
There is no (9, 57, 4166)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 6 083886 754444 381977 586347 050969 216672 436197 382972 083746 986274 793472 405142 042051 706509 961765 789634 442854 437121 > 8157 [i]