Best Known (20, 20+81, s)-Nets in Base 7
(20, 20+81, 28)-Net over F7 — Constructive and digital
Digital (20, 101, 28)-net over F7, using
- net from sequence [i] based on digital (20, 27)-sequence over F7, using
(20, 20+81, 54)-Net over F7 — Digital
Digital (20, 101, 54)-net over F7, using
- t-expansion [i] based on digital (19, 101, 54)-net over F7, using
- net from sequence [i] based on digital (19, 53)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 19 and N(F) ≥ 54, using
- net from sequence [i] based on digital (19, 53)-sequence over F7, using
(20, 20+81, 297)-Net in Base 7 — Upper bound on s
There is no (20, 101, 298)-net in base 7, because
- 3 times m-reduction [i] would yield (20, 98, 298)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(798, 298, S7, 78), but
- 2 times code embedding in larger space [i] would yield OA(7100, 300, S7, 78), but
- the linear programming bound shows that M ≥ 299097 729323 432107 658998 976145 469331 941961 894022 216549 209038 748595 069982 624063 065575 074764 631986 741422 150045 473563 595890 143444 448284 396875 634601 537987 034825 113560 978343 299483 531225 583322 370955 044379 993698 808897 633017 272275 741400 124664 486067 392877 939803 924304 569369 238729 096341 165832 873108 473306 301216 512000 / 68971 115940 400442 507083 549705 418604 164721 288198 777680 661522 163060 434192 960842 312243 374594 267039 403788 339442 856100 789559 193568 709409 193229 298849 279972 701166 845648 383006 691812 079567 150519 208227 381024 392383 318726 624445 756429 > 7100 [i]
- 2 times code embedding in larger space [i] would yield OA(7100, 300, S7, 78), but
- extracting embedded orthogonal array [i] would yield OA(798, 298, S7, 78), but