Best Known (70−62, 70, s)-Nets in Base 8
(70−62, 70, 35)-Net over F8 — Constructive and digital
Digital (8, 70, 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]
(70−62, 70, 74)-Net in Base 8 — Upper bound on s
There is no (8, 70, 75)-net in base 8, because
- 5 times m-reduction [i] would yield (8, 65, 75)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(865, 75, S8, 57), but
- the linear programming bound shows that M ≥ 79731 645809 253852 875349 975880 953007 494669 461217 895054 958252 785664 / 1 241577 > 865 [i]
- extracting embedded orthogonal array [i] would yield OA(865, 75, S8, 57), but