Best Known (135−73, 135, s)-Nets in Base 9
(135−73, 135, 128)-Net over F9 — Constructive and digital
Digital (62, 135, 128)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (13, 49, 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, 86, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9 (see above)
- digital (13, 49, 64)-net over F9, using
(135−73, 135, 192)-Net over F9 — Digital
Digital (62, 135, 192)-net over F9, using
- t-expansion [i] based on digital (61, 135, 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
(135−73, 135, 6339)-Net in Base 9 — Upper bound on s
There is no (62, 135, 6340)-net in base 9, because
- 1 times m-reduction [i] would yield (62, 134, 6340)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 74 134664 310961 247510 778302 555119 000307 216452 803970 034066 848495 696563 110239 449403 191712 058253 503564 185255 851957 839398 437715 895169 > 9134 [i]