Best Known (8, 8+41, s)-Nets in Base 8
(8, 8+41, 35)-Net over F8 — Constructive and digital
Digital (8, 49, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
(8, 8+41, 142)-Net in Base 8 — Upper bound on s
There is no (8, 49, 143)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(849, 143, S8, 41), but
- the linear programming bound shows that M ≥ 55093 361917 380284 610814 636080 006957 080132 913574 062040 734204 107898 287002 099836 564155 743863 357789 394314 461184 / 293 535454 109068 710912 094666 727817 106190 331626 683390 630307 979677 > 849 [i]