Best Known (48−40, 48, s)-Nets in Base 8
(48−40, 48, 35)-Net over F8 — Constructive and digital
Digital (8, 48, 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]
(48−40, 48, 145)-Net in Base 8 — Upper bound on s
There is no (8, 48, 146)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(848, 146, S8, 40), but
- the linear programming bound shows that M ≥ 107 581771 175514 062772 763511 919315 307624 483671 347421 730272 953235 380344 858247 031315 978764 107653 316608 / 4 502794 653751 932691 218701 873039 748265 279176 294201 497971 > 848 [i]