Best Known (49−39, 49, s)-Nets in Base 8
(49−39, 49, 46)-Net over F8 — Constructive and digital
Digital (10, 49, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
(49−39, 49, 199)-Net in Base 8 — Upper bound on s
There is no (10, 49, 200)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(849, 200, S8, 39), but
- the linear programming bound shows that M ≥ 7468 344533 001076 528285 902269 380991 196716 305212 808512 515996 474106 819103 980072 266482 346203 545600 / 39 419180 895524 740911 560231 322271 789894 668181 749389 > 849 [i]