Best Known (135−69, 135, s)-Nets in Base 9
(135−69, 135, 165)-Net over F9 — Constructive and digital
Digital (66, 135, 165)-net over F9, using
- t-expansion [i] based on digital (64, 135, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(135−69, 135, 230)-Net over F9 — Digital
Digital (66, 135, 230)-net over F9, using
(135−69, 135, 9734)-Net in Base 9 — Upper bound on s
There is no (66, 135, 9735)-net in base 9, because
- 1 times m-reduction [i] would yield (66, 134, 9735)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 74 086280 651885 177696 036372 331283 165379 035221 281034 582381 786526 967688 282351 068635 564741 864435 114429 266377 860633 706534 867741 638257 > 9134 [i]