Best Known (58−48, 58, s)-Nets in Base 8
(58−48, 58, 46)-Net over F8 — Constructive and digital
Digital (10, 58, 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]
(58−48, 58, 170)-Net in Base 8 — Upper bound on s
There is no (10, 58, 171)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(858, 171, S8, 48), but
- the linear programming bound shows that M ≥ 138482 785270 511117 139260 798345 761181 716506 774131 995617 401225 404899 740610 466777 512621 912213 715712 116699 879104 781358 774121 387786 240000 / 5 389108 729495 661193 674579 886941 842618 639299 665059 027976 860691 064956 765196 590003 > 858 [i]