Best Known (124, 179, s)-Nets in Base 3
(124, 179, 192)-Net over F3 — Constructive and digital
Digital (124, 179, 192)-net over F3, using
- 1 times m-reduction [i] based on digital (124, 180, 192)-net over F3, using
- trace code for nets [i] based on digital (4, 60, 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
- trace code for nets [i] based on digital (4, 60, 64)-net over F27, using
(124, 179, 373)-Net over F3 — Digital
Digital (124, 179, 373)-net over F3, using
(124, 179, 7609)-Net in Base 3 — Upper bound on s
There is no (124, 179, 7610)-net in base 3, because
- 1 times m-reduction [i] would yield (124, 178, 7610)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 8 490158 318336 059956 086524 067129 369824 638233 892623 282308 883700 650559 068112 920381 191681 > 3178 [i]