Best Known (92, 165, s)-Nets in Base 3
(92, 165, 80)-Net over F3 — Constructive and digital
Digital (92, 165, 80)-net over F3, using
- 3 times m-reduction [i] based on digital (92, 168, 80)-net over F3, using
- trace code for nets [i] based on digital (8, 84, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- trace code for nets [i] based on digital (8, 84, 40)-net over F9, using
(92, 165, 120)-Net over F3 — Digital
Digital (92, 165, 120)-net over F3, using
(92, 165, 1029)-Net in Base 3 — Upper bound on s
There is no (92, 165, 1030)-net in base 3, because
- 1 times m-reduction [i] would yield (92, 164, 1030)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 783808 426470 498223 378408 009973 256144 632668 909830 987671 032931 018956 900746 975305 > 3164 [i]