Best Known (6, 6+43, s)-Nets in Base 9
(6, 6+43, 34)-Net over F9 — Constructive and digital
Digital (6, 49, 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+43, 35)-Net over F9 — Digital
Digital (6, 49, 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+43, 107)-Net in Base 9 — Upper bound on s
There is no (6, 49, 108)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(949, 108, S9, 43), but
- the linear programming bound shows that M ≥ 7517 398651 006612 088893 064619 371693 848978 214883 758512 281909 891904 493412 866646 797962 307821 277061 / 125718 746341 734854 627467 141668 369955 854411 432962 > 949 [i]