Best Known (149−63, 149, s)-Nets in Base 3
(149−63, 149, 80)-Net over F3 — Constructive and digital
Digital (86, 149, 80)-net over F3, using
- 7 times m-reduction [i] based on digital (86, 156, 80)-net over F3, using
- trace code for nets [i] based on digital (8, 78, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- trace code for nets [i] based on digital (8, 78, 40)-net over F9, using
(149−63, 149, 124)-Net over F3 — Digital
Digital (86, 149, 124)-net over F3, using
(149−63, 149, 1147)-Net in Base 3 — Upper bound on s
There is no (86, 149, 1148)-net in base 3, because
- 1 times m-reduction [i] would yield (86, 148, 1148)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 42112 349227 039618 353203 938662 896644 472810 534868 440603 320171 264068 599121 > 3148 [i]