Best Known (54−48, 54, s)-Nets in Base 9
(54−48, 54, 34)-Net over F9 — Constructive and digital
Digital (6, 54, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
(54−48, 54, 35)-Net over F9 — Digital
Digital (6, 54, 35)-net over F9, using
- net from sequence [i] based on digital (6, 34)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 35, using
(54−48, 54, 82)-Net in Base 9 — Upper bound on s
There is no (6, 54, 83)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(954, 83, S9, 48), but
- the linear programming bound shows that M ≥ 10132 927410 689078 360872 417149 617665 028299 664062 593121 142935 280521 657389 / 2 927120 765949 062837 > 954 [i]