Best Known (127−65, 127, s)-Nets in Base 3
(127−65, 127, 56)-Net over F3 — Constructive and digital
Digital (62, 127, 56)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (15, 47, 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, 80, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3 (see above)
- digital (15, 47, 28)-net over F3, using
(127−65, 127, 64)-Net over F3 — Digital
Digital (62, 127, 64)-net over F3, using
- t-expansion [i] based on digital (49, 127, 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
(127−65, 127, 452)-Net in Base 3 — Upper bound on s
There is no (62, 127, 453)-net in base 3, because
- 1 times m-reduction [i] would yield (62, 126, 453)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 313524 283828 325789 282965 060553 531080 019120 593458 199015 028609 > 3126 [i]