Best Known (89, 89+154, s)-Nets in Base 3
(89, 89+154, 64)-Net over F3 — Constructive and digital
Digital (89, 243, 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+154, 96)-Net over F3 — Digital
Digital (89, 243, 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+154, 400)-Net in Base 3 — Upper bound on s
There is no (89, 243, 401)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 92 193850 871551 152221 658554 317449 172298 687757 149770 939174 476329 249793 182435 953783 055477 386763 956718 570576 193180 497139 > 3243 [i]