Best Known (89, 89+130, s)-Nets in Base 3
(89, 89+130, 64)-Net over F3 — Constructive and digital
Digital (89, 219, 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+130, 96)-Net over F3 — Digital
Digital (89, 219, 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+130, 445)-Net in Base 3 — Upper bound on s
There is no (89, 219, 446)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 311 229861 649273 170811 307928 831692 623115 409637 716404 122845 908233 249711 777529 945049 609815 015963 703160 431357 > 3219 [i]