Best Known (65−57, 65, s)-Nets in Base 9
(65−57, 65, 40)-Net over F9 — Constructive and digital
Digital (8, 65, 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
(65−57, 65, 42)-Net over F9 — Digital
Digital (8, 65, 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
(65−57, 65, 115)-Net in Base 9 — Upper bound on s
There is no (8, 65, 116)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(965, 116, S9, 57), but
- the linear programming bound shows that M ≥ 6 495520 473631 853646 214005 627804 277933 207941 122153 635068 011997 733145 247620 083893 167909 673565 248879 284590 891131 508581 / 59006 138064 996169 643698 040417 343383 357764 190144 925271 > 965 [i]