Best Known (89, 89+146, s)-Nets in Base 3
(89, 89+146, 64)-Net over F3 — Constructive and digital
Digital (89, 235, 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+146, 96)-Net over F3 — Digital
Digital (89, 235, 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+146, 412)-Net in Base 3 — Upper bound on s
There is no (89, 235, 413)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 13831 671450 693225 679805 888523 298758 443367 575771 376637 568535 487182 045667 013542 763497 149978 430810 448099 182749 641499 > 3235 [i]