Best Known (6, 6+42, s)-Nets in Base 9
(6, 6+42, 34)-Net over F9 — Constructive and digital
Digital (6, 48, 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
(6, 6+42, 35)-Net over F9 — Digital
Digital (6, 48, 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
(6, 6+42, 113)-Net in Base 9 — Upper bound on s
There is no (6, 48, 114)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(948, 114, S9, 42), but
- the linear programming bound shows that M ≥ 178742 922548 708302 342120 089759 575955 416976 881295 942542 289756 659383 343611 785195 039633 / 26 770378 203904 826707 556512 572145 603142 > 948 [i]