Best Known (69, 69+78, s)-Nets in Base 9
(69, 69+78, 165)-Net over F9 — Constructive and digital
Digital (69, 147, 165)-net over F9, using
- t-expansion [i] based on digital (64, 147, 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+78, 212)-Net over F9 — Digital
Digital (69, 147, 212)-net over F9, using
(69, 69+78, 7581)-Net in Base 9 — Upper bound on s
There is no (69, 147, 7582)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 188 665976 308554 315822 500236 994827 334555 990064 846766 794946 835583 176462 651803 191464 277761 894263 194797 661575 617303 504723 123288 323488 433451 894225 > 9147 [i]