Best Known (18, 75, s)-Nets in Base 5
(18, 75, 43)-Net over F5 — Constructive and digital
Digital (18, 75, 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]
(18, 75, 128)-Net in Base 5 — Upper bound on s
There is no (18, 75, 129)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(575, 129, S5, 57), but
- the linear programming bound shows that M ≥ 15834 198365 926459 174495 070912 926342 657353 410478 689511 253355 057565 629427 594446 047272 749174 340367 965858 719674 965607 825123 381502 407937 659882 009029 388427 734375 / 572218 660816 232995 700333 092801 376621 539128 291687 038229 804061 092293 114083 215457 939111 033787 669855 680572 > 575 [i]