Best Known (85, 85+58, s)-Nets in Base 3
(85, 85+58, 128)-Net over F3 — Constructive and digital
Digital (85, 143, 128)-net over F3, using
- 1 times m-reduction [i] based on digital (85, 144, 128)-net over F3, using
- trace code for nets [i] based on digital (13, 72, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- trace code for nets [i] based on digital (13, 72, 64)-net over F9, using
(85, 85+58, 135)-Net over F3 — Digital
Digital (85, 143, 135)-net over F3, using
(85, 85+58, 1286)-Net in Base 3 — Upper bound on s
There is no (85, 143, 1287)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 171 602636 669274 035377 887135 237850 391465 858461 571510 893348 695105 036055 > 3143 [i]