Best Known (142−57, 142, s)-Nets in Base 3
(142−57, 142, 128)-Net over F3 — Constructive and digital
Digital (85, 142, 128)-net over F3, using
- 2 times m-reduction [i] based on digital (85, 144, 128)-net over F3, using
- trace code for nets [i] based on digital (13, 72, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- trace code for nets [i] based on digital (13, 72, 64)-net over F9, using
(142−57, 142, 139)-Net over F3 — Digital
Digital (85, 142, 139)-net over F3, using
(142−57, 142, 1400)-Net in Base 3 — Upper bound on s
There is no (85, 142, 1401)-net in base 3, because
- 1 times m-reduction [i] would yield (85, 141, 1401)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 19 031884 071915 515039 077937 638623 037274 448910 636057 711380 933337 196145 > 3141 [i]