Best Known (142, 142+78, s)-Nets in Base 3
(142, 142+78, 162)-Net over F3 — Constructive and digital
Digital (142, 220, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 110, 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
(142, 142+78, 287)-Net over F3 — Digital
Digital (142, 220, 287)-net over F3, using
(142, 142+78, 3744)-Net in Base 3 — Upper bound on s
There is no (142, 220, 3745)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 928 351066 674538 924325 463436 325377 141160 207390 428547 632109 093007 240235 780114 290790 782764 546490 661143 208587 > 3220 [i]