Best Known (31, 147, s)-Nets in Base 9
(31, 147, 78)-Net over F9 — Constructive and digital
Digital (31, 147, 78)-net over F9, using
- t-expansion [i] based on digital (22, 147, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the 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) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(31, 147, 120)-Net over F9 — Digital
Digital (31, 147, 120)-net over F9, using
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 31 and N(F) ≥ 120, using
(31, 147, 700)-Net in Base 9 — Upper bound on s
There is no (31, 147, 701)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 197 531694 603154 476360 353637 410229 581417 739421 218880 002967 135945 114915 438385 463383 066972 602230 524463 785935 810405 495436 693146 312389 491769 583185 > 9147 [i]