Best Known (86, 123, s)-Nets in Base 3
(86, 123, 192)-Net over F3 — Constructive and digital
Digital (86, 123, 192)-net over F3, using
- trace code for nets [i] based on digital (4, 41, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
(86, 123, 293)-Net over F3 — Digital
Digital (86, 123, 293)-net over F3, using
(86, 123, 6452)-Net in Base 3 — Upper bound on s
There is no (86, 123, 6453)-net in base 3, because
- 1 times m-reduction [i] would yield (86, 122, 6453)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 16182 892382 492489 648885 398182 388109 566488 821497 085414 745457 > 3122 [i]