Best Known (49−41, 49, s)-Nets in Base 81
(49−41, 49, 172)-Net over F81 — Constructive and digital
Digital (8, 49, 172)-net over F81, using
- t-expansion [i] based on digital (7, 49, 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
(49−41, 49, 226)-Net over F81 — Digital
Digital (8, 49, 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
(49−41, 49, 3940)-Net in Base 81 — Upper bound on s
There is no (8, 49, 3941)-net in base 81, because
- 1 times m-reduction [i] would yield (8, 48, 3941)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 40 668252 447498 194969 501219 568595 473189 359361 803840 800782 135581 134501 930349 351258 554401 761601 > 8148 [i]