Best Known (84, 137, s)-Nets in Base 3
(84, 137, 128)-Net over F3 — Constructive and digital
Digital (84, 137, 128)-net over F3, using
- 5 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, 137, 149)-Net over F3 — Digital
Digital (84, 137, 149)-net over F3, using
(84, 137, 1626)-Net in Base 3 — Upper bound on s
There is no (84, 137, 1627)-net in base 3, because
- 1 times m-reduction [i] would yield (84, 136, 1627)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 77933 518518 318197 566295 165647 280627 030311 384545 003679 430747 793765 > 3136 [i]