Best Known (180−58, 180, s)-Nets in Base 3
(180−58, 180, 162)-Net over F3 — Constructive and digital
Digital (122, 180, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 90, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(180−58, 180, 324)-Net over F3 — Digital
Digital (122, 180, 324)-net over F3, using
(180−58, 180, 5311)-Net in Base 3 — Upper bound on s
There is no (122, 180, 5312)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 76 393647 323702 420985 291068 770129 907500 626009 285048 223269 864766 693753 898080 143257 867649 > 3180 [i]