Best Known (57−45, 57, s)-Nets in Base 81
(57−45, 57, 172)-Net over F81 — Constructive and digital
Digital (12, 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
(57−45, 57, 298)-Net over F81 — Digital
Digital (12, 57, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
(57−45, 57, 8149)-Net in Base 81 — Upper bound on s
There is no (12, 57, 8150)-net in base 81, because
- 1 times m-reduction [i] would yield (12, 56, 8150)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 75041 361651 959388 267447 098261 413595 897755 817422 359188 265554 134463 085694 214446 162671 535376 008472 529550 824001 > 8156 [i]