Best Known (57−51, 57, s)-Nets in Base 81
(57−51, 57, 160)-Net over F81 — Constructive and digital
Digital (6, 57, 160)-net over F81, using
- t-expansion [i] based on digital (5, 57, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(57−51, 57, 190)-Net over F81 — Digital
Digital (6, 57, 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
(57−51, 57, 2384)-Net in Base 81 — Upper bound on s
There is no (6, 57, 2385)-net in base 81, because
- 1 times m-reduction [i] would yield (6, 56, 2385)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 75799 086891 319457 777613 595631 822271 197488 642322 133343 521241 852255 076913 238572 212566 054901 816863 491790 370001 > 8156 [i]