Best Known (163, 163+83, s)-Nets in Base 3
(163, 163+83, 162)-Net over F3 — Constructive and digital
Digital (163, 246, 162)-net over F3, using
- t-expansion [i] based on digital (157, 246, 162)-net over F3, using
- 4 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
- 4 times m-reduction [i] based on digital (157, 250, 162)-net over F3, using
(163, 163+83, 367)-Net over F3 — Digital
Digital (163, 246, 367)-net over F3, using
(163, 163+83, 5687)-Net in Base 3 — Upper bound on s
There is no (163, 246, 5688)-net in base 3, because
- 1 times m-reduction [i] would yield (163, 245, 5688)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 789 056892 727564 578735 268212 335010 453441 176687 731666 405160 689102 348310 294643 560158 645717 720012 356509 789916 396333 083889 > 3245 [i]