Best Known (10, 10+45, s)-Nets in Base 8
(10, 10+45, 46)-Net over F8 — Constructive and digital
Digital (10, 55, 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]
(10, 10+45, 182)-Net in Base 8 — Upper bound on s
There is no (10, 55, 183)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(855, 183, S8, 45), but
- the linear programming bound shows that M ≥ 2 546482 465755 818649 531271 647222 741248 758036 995469 611923 990581 409456 155013 443230 902056 642362 493622 536267 366400 000000 / 53625 940387 853029 735674 263930 801743 376240 811734 873353 891572 203359 > 855 [i]