Best Known (129, 129+65, s)-Nets in Base 3
(129, 129+65, 162)-Net over F3 — Constructive and digital
Digital (129, 194, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 97, 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
(129, 129+65, 305)-Net over F3 — Digital
Digital (129, 194, 305)-net over F3, using
(129, 129+65, 4793)-Net in Base 3 — Upper bound on s
There is no (129, 194, 4794)-net in base 3, because
- 1 times m-reduction [i] would yield (129, 193, 4794)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 121 869716 423871 246282 668178 689258 649813 518597 423062 597921 170266 918873 792768 046213 022863 881025 > 3193 [i]