Best Known (89, 89+124, s)-Nets in Base 3
(89, 89+124, 64)-Net over F3 — Constructive and digital
Digital (89, 213, 64)-net over F3, using
- net from sequence [i] based on digital (89, 63)-sequence over F3, using
- base reduction for sequences [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
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
(89, 89+124, 96)-Net over F3 — Digital
Digital (89, 213, 96)-net over F3, using
- net from sequence [i] based on digital (89, 95)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 89 and N(F) ≥ 96, using
(89, 89+124, 462)-Net in Base 3 — Upper bound on s
There is no (89, 213, 463)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 440609 827433 824674 134358 177669 841056 716584 261868 029764 984482 820407 435147 751872 868047 369537 273546 631333 > 3213 [i]