Best Known (72−54, 72, s)-Nets in Base 5
(72−54, 72, 43)-Net over F5 — Constructive and digital
Digital (18, 72, 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]
(72−54, 72, 145)-Net in Base 5 — Upper bound on s
There is no (18, 72, 146)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(572, 146, S5, 54), but
- the linear programming bound shows that M ≥ 2 337987 104589 205975 244521 874706 709110 308098 467912 457938 395144 635190 986720 981640 145896 922691 158719 812153 706188 200190 704556 517568 750394 862562 088588 219685 307326 681605 251337 396006 508388 308618 034454 496562 834717 542484 480496 169312 758260 302363 734568 740992 517837 080726 626763 915731 999077 252112 329006 195068 359375 / 10203 002290 413663 539277 092847 600779 230787 578018 907642 106711 864194 686055 673736 241580 628185 946432 791899 701859 667098 199648 388316 747874 707301 423918 103421 969311 192272 854088 288813 619231 443732 977414 730300 111593 550629 499259 687632 054739 025771 147071 634027 933318 > 572 [i]