Best Known (51−39, 51, s)-Nets in Base 81
(51−39, 51, 172)-Net over F81 — Constructive and digital
Digital (12, 51, 172)-net over F81, using
- t-expansion [i] based on digital (7, 51, 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
(51−39, 51, 298)-Net over F81 — Digital
Digital (12, 51, 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
(51−39, 51, 10424)-Net in Base 81 — Upper bound on s
There is no (12, 51, 10425)-net in base 81, because
- 1 times m-reduction [i] would yield (12, 50, 10425)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 265685 264337 800463 505586 755634 057208 648966 317441 865020 392261 492537 903244 585242 031330 813499 206001 > 8150 [i]