Best Known (57−49, 57, s)-Nets in Base 81
(57−49, 57, 172)-Net over F81 — Constructive and digital
Digital (8, 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
(57−49, 57, 226)-Net over F81 — Digital
Digital (8, 57, 226)-net over F81, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
(57−49, 57, 3466)-Net in Base 81 — Upper bound on s
There is no (8, 57, 3467)-net in base 81, because
- 1 times m-reduction [i] would yield (8, 56, 3467)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 75116 865061 863494 989700 325161 853551 158000 036489 355628 601364 199940 215069 549440 367849 539999 864200 079207 987841 > 8156 [i]