Best Known (50−42, 50, s)-Nets in Base 9
(50−42, 50, 40)-Net over F9 — Constructive and digital
Digital (8, 50, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
(50−42, 50, 42)-Net over F9 — Digital
Digital (8, 50, 42)-net over F9, using
- net from sequence [i] based on digital (8, 41)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 42, using
(50−42, 50, 171)-Net in Base 9 — Upper bound on s
There is no (8, 50, 172)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(950, 172, S9, 42), but
- the linear programming bound shows that M ≥ 89024 049000 236532 225400 329419 774420 888658 495570 632071 673903 786531 708850 238046 819165 038530 528671 563125 / 170223 945583 155937 857482 287753 245984 186508 179709 835797 > 950 [i]