Best Known (187−98, 187, s)-Nets in Base 3
(187−98, 187, 64)-Net over F3 — Constructive and digital
Digital (89, 187, 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
(187−98, 187, 96)-Net over F3 — Digital
Digital (89, 187, 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
(187−98, 187, 585)-Net in Base 3 — Upper bound on s
There is no (89, 187, 586)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 172019 828186 874476 228340 349466 560330 221363 778097 669443 285053 048500 526705 736887 484781 024181 > 3187 [i]