Best Known (142−42, 142, s)-Nets in Base 3
(142−42, 142, 204)-Net over F3 — Constructive and digital
Digital (100, 142, 204)-net over F3, using
- 31 times duplication [i] based on digital (99, 141, 204)-net over F3, using
- trace code for nets [i] based on digital (5, 47, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- trace code for nets [i] based on digital (5, 47, 68)-net over F27, using
(142−42, 142, 348)-Net over F3 — Digital
Digital (100, 142, 348)-net over F3, using
(142−42, 142, 7286)-Net in Base 3 — Upper bound on s
There is no (100, 142, 7287)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 56 545925 607977 014598 868773 254472 442227 862092 041544 112659 755558 250375 > 3142 [i]