Best Known (134, 134+68, s)-Nets in Base 3
(134, 134+68, 162)-Net over F3 — Constructive and digital
Digital (134, 202, 162)-net over F3, using
- 2 times m-reduction [i] based on digital (134, 204, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 102, 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, 102, 81)-net over F9, using
(134, 134+68, 311)-Net over F3 — Digital
Digital (134, 202, 311)-net over F3, using
(134, 134+68, 4591)-Net in Base 3 — Upper bound on s
There is no (134, 202, 4592)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 398436 760977 578840 520758 674308 770237 724055 012992 778167 712606 453067 171988 572819 803809 820392 632737 > 3202 [i]