Best Known (116−85, 116, s)-Nets in Base 5
(116−85, 116, 72)-Net over F5 — Constructive and digital
Digital (31, 116, 72)-net over F5, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 31 and N(F) ≥ 72, using
(116−85, 116, 296)-Net in Base 5 — Upper bound on s
There is no (31, 116, 297)-net in base 5, because
- 2 times m-reduction [i] would yield (31, 114, 297)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5114, 297, S5, 83), but
- 3 times code embedding in larger space [i] would yield OA(5117, 300, S5, 83), but
- the linear programming bound shows that M ≥ 3 416602 485600 917363 497745 059945 611059 566209 000772 725113 568664 369939 577158 289674 207552 727630 789798 594401 885800 783085 280034 536305 147808 147621 534359 670577 109597 990440 531848 872966 763881 264763 629237 216824 214511 543844 807078 221776 277824 907241 366096 573006 050944 236569 658673 034193 649391 262108 286983 680440 734701 470155 156683 649605 434469 859544 089144 259750 717713 686185 561527 963727 712631 225585 937500 000000 / 491 377629 702850 501744 888693 301798 080890 888692 090032 689031 761120 944400 103125 740433 698388 038363 119813 267025 808724 195150 452197 626754 769172 757005 064735 578599 590639 752026 497923 094809 029144 287706 497457 008281 804861 212179 256256 309134 696173 099757 427884 433578 137601 803252 471566 065133 312365 473203 113532 559164 207353 716213 > 5117 [i]
- 3 times code embedding in larger space [i] would yield OA(5117, 300, S5, 83), but
- extracting embedded orthogonal array [i] would yield OA(5114, 297, S5, 83), but