Best Known (37−31, 37, s)-Nets in Base 81
(37−31, 37, 160)-Net over F81 — Constructive and digital
Digital (6, 37, 160)-net over F81, using
- t-expansion [i] based on digital (5, 37, 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
(37−31, 37, 190)-Net over F81 — Digital
Digital (6, 37, 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
(37−31, 37, 3048)-Net in Base 81 — Upper bound on s
There is no (6, 37, 3049)-net in base 81, because
- 1 times m-reduction [i] would yield (6, 36, 3049)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 509 967717 897147 010669 469650 169718 613250 901612 533267 817748 962634 858801 > 8136 [i]