Best Known (73−55, 73, s)-Nets in Base 5
(73−55, 73, 43)-Net over F5 — Constructive and digital
Digital (18, 73, 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]
(73−55, 73, 139)-Net in Base 5 — Upper bound on s
There is no (18, 73, 140)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(573, 140, S5, 55), but
- the linear programming bound shows that M ≥ 12 773589 885555 808584 662591 353486 711183 881432 889243 787748 130568 000597 820804 547794 329266 960072 175926 141225 138841 844844 715103 101415 348202 859214 100140 061565 868657 002057 335272 135315 132524 092965 840828 111073 939590 994451 791793 566854 534590 860713 259692 391465 839611 530697 084162 966348 230838 775634 765625 / 11630 570805 954385 046480 662157 243618 744892 843167 947243 671058 734689 059803 938788 850690 289976 938529 289444 317796 118938 854972 789067 806344 015623 627195 303164 171478 948959 131361 738284 201064 582445 829586 006079 471662 786488 339600 600031 516987 849797 027033 > 573 [i]