Best Known (57−47, 57, s)-Nets in Base 81
(57−47, 57, 172)-Net over F81 — Constructive and digital
Digital (10, 57, 172)-net over F81, using
- t-expansion [i] based on digital (7, 57, 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
(57−47, 57, 244)-Net over F81 — Digital
Digital (10, 57, 244)-net over F81, using
- t-expansion [i] based on digital (9, 57, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
(57−47, 57, 5214)-Net in Base 81 — Upper bound on s
There is no (10, 57, 5215)-net in base 81, because
- 1 times m-reduction [i] would yield (10, 56, 5215)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 75337 617662 422378 441407 109090 846374 934886 941632 973908 175921 974545 276481 957380 902447 680038 410012 833165 179601 > 8156 [i]