Best Known (58−41, 58, s)-Nets in Base 4
(58−41, 58, 33)-Net over F4 — Constructive and digital
Digital (17, 58, 33)-net over F4, using
- t-expansion [i] based on digital (15, 58, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
(58−41, 58, 40)-Net over F4 — Digital
Digital (17, 58, 40)-net over F4, using
- net from sequence [i] based on digital (17, 39)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 17 and N(F) ≥ 40, using
(58−41, 58, 109)-Net in Base 4 — Upper bound on s
There is no (17, 58, 110)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(458, 110, S4, 41), but
- the linear programming bound shows that M ≥ 1232 155961 216230 168086 977678 056475 191089 409710 805770 829825 897828 417067 677196 009558 961106 027628 461497 995772 222254 044023 160230 949557 990006 504845 840607 997118 369373 847851 273455 403008 / 13446 810158 281327 760184 995983 919490 800441 646762 168115 151101 794360 608708 987818 154852 821096 884734 101312 394526 499211 581201 357552 019470 400051 102575 > 458 [i]