Best Known (84, 139, s)-Nets in Base 3
(84, 139, 128)-Net over F3 — Constructive and digital
Digital (84, 139, 128)-net over F3, using
- 3 times m-reduction [i] based on digital (84, 142, 128)-net over F3, using
- trace code for nets [i] based on digital (13, 71, 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, 71, 64)-net over F9, using
(84, 139, 142)-Net over F3 — Digital
Digital (84, 139, 142)-net over F3, using
(84, 139, 1473)-Net in Base 3 — Upper bound on s
There is no (84, 139, 1474)-net in base 3, because
- 1 times m-reduction [i] would yield (84, 138, 1474)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 704181 755399 085186 584702 939069 411072 462185 684897 939540 859946 686433 > 3138 [i]