Best Known (239−150, 239, s)-Nets in Base 3
(239−150, 239, 64)-Net over F3 — Constructive and digital
Digital (89, 239, 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
(239−150, 239, 96)-Net over F3 — Digital
Digital (89, 239, 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
(239−150, 239, 406)-Net in Base 3 — Upper bound on s
There is no (89, 239, 407)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 184964 798766 263817 895777 552247 680910 560609 181519 801013 859209 558449 584235 265234 166700 281017 707292 393714 651596 228171 > 3239 [i]