Best Known (89, 89+144, s)-Nets in Base 3
(89, 89+144, 64)-Net over F3 — Constructive and digital
Digital (89, 233, 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+144, 96)-Net over F3 — Digital
Digital (89, 233, 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+144, 416)-Net in Base 3 — Upper bound on s
There is no (89, 233, 417)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1674 198554 780025 798065 899374 321710 238351 777139 235149 912528 394714 091170 335350 203456 766997 951328 313190 859629 952673 > 3233 [i]