Best Known (19, 19+57, s)-Nets in Base 5
(19, 19+57, 43)-Net over F5 — Constructive and digital
Digital (19, 76, 43)-net over F5, using
- t-expansion [i] based on digital (18, 76, 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]
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
(19, 19+57, 45)-Net over F5 — Digital
Digital (19, 76, 45)-net over F5, using
- net from sequence [i] based on digital (19, 44)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 19 and N(F) ≥ 45, using
(19, 19+57, 148)-Net in Base 5 — Upper bound on s
There is no (19, 76, 149)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(576, 149, S5, 57), but
- the linear programming bound shows that M ≥ 780503 587553 223889 720415 027567 336992 511261 258385 815168 846450 570765 144209 000202 823481 156584 132306 854590 511456 736304 498550 323790 536763 627888 572048 333760 759249 039907 711854 816156 556522 450960 037276 519906 389033 493516 022634 698874 722039 553885 726823 681910 821441 368927 282568 838903 179113 220762 988176 182339 827846 590196 713805 198669 433593 750000 / 5 775356 774777 123485 240953 732172 774287 605136 317645 043648 216709 150189 510322 103703 748418 849559 548240 298208 840653 550830 739022 466463 734298 631974 620549 171164 159951 052318 911861 347605 706735 306068 519914 619543 051574 871140 761966 035585 243891 160744 983792 939332 641846 757954 046735 609675 598469 > 576 [i]