Best Known (63, 63+73, s)-Nets in Base 9
(63, 63+73, 128)-Net over F9 — Constructive and digital
Digital (63, 136, 128)-net over F9, using
- 1 times m-reduction [i] based on digital (63, 137, 128)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (13, 50, 64)-net over F9, using
- net from sequence [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
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (13, 87, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9 (see above)
- digital (13, 50, 64)-net over F9, using
- (u, u+v)-construction [i] based on
(63, 63+73, 192)-Net over F9 — Digital
Digital (63, 136, 192)-net over F9, using
- t-expansion [i] based on digital (61, 136, 192)-net over F9, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
(63, 63+73, 6739)-Net in Base 9 — Upper bound on s
There is no (63, 136, 6740)-net in base 9, because
- 1 times m-reduction [i] would yield (63, 135, 6740)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 665 827447 797388 516202 063785 430878 300802 225511 270844 238649 174166 334733 152702 917262 452333 704059 772844 867469 205637 022102 822132 093313 > 9135 [i]