Best Known (6, 6+37, s)-Nets in Base 9
(6, 6+37, 34)-Net over F9 — Constructive and digital
Digital (6, 43, 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+37, 35)-Net over F9 — Digital
Digital (6, 43, 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+37, 127)-Net in Base 9 — Upper bound on s
There is no (6, 43, 128)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(943, 128, S9, 37), but
- the linear programming bound shows that M ≥ 816642 496462 225155 696478 814469 701648 862208 616549 454564 868674 193133 968234 114768 800000 / 7 101086 752074 399500 226965 505212 822195 355881 > 943 [i]