Best Known (69, 69+73, s)-Nets in Base 9
(69, 69+73, 165)-Net over F9 — Constructive and digital
Digital (69, 142, 165)-net over F9, using
- t-expansion [i] based on digital (64, 142, 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
(69, 69+73, 235)-Net over F9 — Digital
Digital (69, 142, 235)-net over F9, using
(69, 69+73, 9730)-Net in Base 9 — Upper bound on s
There is no (69, 142, 9731)-net in base 9, because
- 1 times m-reduction [i] would yield (69, 141, 9731)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 354 533309 536750 132623 154644 795013 581015 400741 149024 075561 538613 869706 011600 414832 617201 020667 953727 302222 504414 564792 045032 223931 839585 > 9141 [i]