Best Known (154, 154+80, s)-Nets in Base 3
(154, 154+80, 162)-Net over F3 — Constructive and digital
Digital (154, 234, 162)-net over F3, using
- 10 times m-reduction [i] based on digital (154, 244, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 122, 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
- trace code for nets [i] based on digital (32, 122, 81)-net over F9, using
(154, 154+80, 338)-Net over F3 — Digital
Digital (154, 234, 338)-net over F3, using
(154, 154+80, 4835)-Net in Base 3 — Upper bound on s
There is no (154, 234, 4836)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 4465 264178 699886 551646 227192 778914 591007 754586 208558 053357 309422 939423 502728 673336 907769 292629 690498 681495 226049 > 3234 [i]