Best Known (157, 157+84, s)-Nets in Base 3
(157, 157+84, 162)-Net over F3 — Constructive and digital
Digital (157, 241, 162)-net over F3, using
- 9 times m-reduction [i] based on digital (157, 250, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 125, 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, 125, 81)-net over F9, using
(157, 157+84, 327)-Net over F3 — Digital
Digital (157, 241, 327)-net over F3, using
(157, 157+84, 4472)-Net in Base 3 — Upper bound on s
There is no (157, 241, 4473)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 9 739729 214351 798367 765874 880744 544519 234400 133150 392622 406916 729401 121606 173844 584185 748872 072273 680155 759749 302233 > 3241 [i]