Best Known (55, 89, s)-Nets in Base 3
(55, 89, 80)-Net over F3 — Constructive and digital
Digital (55, 89, 80)-net over F3, using
- 5 times m-reduction [i] based on digital (55, 94, 80)-net over F3, using
- trace code for nets [i] based on digital (8, 47, 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, 47, 40)-net over F9, using
(55, 89, 110)-Net over F3 — Digital
Digital (55, 89, 110)-net over F3, using
(55, 89, 1112)-Net in Base 3 — Upper bound on s
There is no (55, 89, 1113)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 916438 023358 219193 008481 634440 417302 225267 > 389 [i]