Best Known (110, 211, s)-Nets in Base 3
(110, 211, 76)-Net over F3 — Constructive and digital
Digital (110, 211, 76)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (15, 65, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- digital (45, 146, 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 (15, 65, 28)-net over F3, using
(110, 211, 118)-Net over F3 — Digital
Digital (110, 211, 118)-net over F3, using
(110, 211, 934)-Net in Base 3 — Upper bound on s
There is no (110, 211, 935)-net in base 3, because
- 1 times m-reduction [i] would yield (110, 210, 935)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 16102 685619 726520 066643 761245 301965 470013 181705 256021 200335 008050 054738 741707 406978 022398 552603 029357 > 3210 [i]