Best Known (1, 1+42, s)-Nets in Base 81
(1, 1+42, 100)-Net over F81 — Constructive and digital
Digital (1, 43, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
(1, 1+42, 508)-Net in Base 81 — Upper bound on s
There is no (1, 43, 509)-net in base 81, because
- 30 times m-reduction [i] would yield (1, 13, 509)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 6 525997 415492 369119 764321 > 8113 [i]