Best Known (52−45, 52, s)-Nets in Base 9
(52−45, 52, 36)-Net over F9 — Constructive and digital
Digital (7, 52, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
(52−45, 52, 40)-Net over F9 — Digital
Digital (7, 52, 40)-net over F9, using
- net from sequence [i] based on digital (7, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 40, using
(52−45, 52, 134)-Net in Base 9 — Upper bound on s
There is no (7, 52, 135)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(952, 135, S9, 45), but
- the linear programming bound shows that M ≥ 307 678596 010045 500261 184865 683684 085259 444971 108112 414856 758831 628199 426942 087105 371006 650847 875198 / 6 847778 079372 524046 620120 165760 594496 964877 651385 > 952 [i]