Best Known (129, 129+116, s)-Nets in Base 3
(129, 129+116, 84)-Net over F3 — Constructive and digital
Digital (129, 245, 84)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (26, 84, 36)-net over F3, using
- net from sequence [i] based on digital (26, 35)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using
- net from sequence [i] based on digital (26, 35)-sequence over F3, using
- digital (45, 161, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- digital (26, 84, 36)-net over F3, using
(129, 129+116, 139)-Net over F3 — Digital
Digital (129, 245, 139)-net over F3, using
(129, 129+116, 1106)-Net in Base 3 — Upper bound on s
There is no (129, 245, 1107)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 793 770132 154564 564260 961459 604144 334656 970485 438368 967302 174875 154843 204849 293185 651340 775334 833334 355489 582876 044565 > 3245 [i]