Best Known (62−44, 62, s)-Nets in Base 5
(62−44, 62, 43)-Net over F5 — Constructive and digital
Digital (18, 62, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
(62−44, 62, 189)-Net in Base 5 — Upper bound on s
There is no (18, 62, 190)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(562, 190, S5, 44), but
- the linear programming bound shows that M ≥ 5 531619 630605 621733 791634 558919 444104 118885 526484 067787 791939 510637 894272 804260 253906 250000 000000 000000 / 236416 842360 352611 941840 260955 732881 660879 805306 461094 587839 > 562 [i]