Best Known (78−71, 78, s)-Nets in Base 81
(78−71, 78, 172)-Net over F81 — Constructive and digital
Digital (7, 78, 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
(78−71, 78, 190)-Net over F81 — Digital
Digital (7, 78, 190)-net over F81, using
- t-expansion [i] based on digital (6, 78, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(78−71, 78, 2725)-Net in Base 81 — Upper bound on s
There is no (7, 78, 2726)-net in base 81, because
- 5 times m-reduction [i] would yield (7, 73, 2726)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 20 968460 341844 295998 051972 245858 343028 439413 859989 347013 400595 638799 143374 498285 996423 532594 205612 883886 405993 199184 782443 225684 746555 727841 > 8173 [i]