Best Known (180−56, 180, s)-Nets in Base 3
(180−56, 180, 192)-Net over F3 — Constructive and digital
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
(180−56, 180, 361)-Net over F3 — Digital
Digital (124, 180, 361)-net over F3, using
(180−56, 180, 6567)-Net in Base 3 — Upper bound on s
There is no (124, 180, 6568)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 76 479877 473726 418003 082197 153824 055247 460854 552699 940355 007222 642048 939581 083747 692097 > 3180 [i]