Best Known (124−63, 124, s)-Nets in Base 3
(124−63, 124, 56)-Net over F3 — Constructive and digital
Digital (61, 124, 56)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (15, 46, 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 (15, 78, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3 (see above)
- digital (15, 46, 28)-net over F3, using
(124−63, 124, 64)-Net over F3 — Digital
Digital (61, 124, 64)-net over F3, using
- t-expansion [i] based on digital (49, 124, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(124−63, 124, 455)-Net in Base 3 — Upper bound on s
There is no (61, 124, 456)-net in base 3, because
- 1 times m-reduction [i] would yield (61, 123, 456)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 49551 495864 851755 054609 083653 107147 664735 448197 406789 136225 > 3123 [i]