Best Known (69−52, 69, s)-Nets in Base 5
(69−52, 69, 42)-Net over F5 — Constructive and digital
Digital (17, 69, 42)-net over F5, using
- net from sequence [i] based on digital (17, 41)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using
(69−52, 69, 136)-Net in Base 5 — Upper bound on s
There is no (17, 69, 137)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(569, 137, S5, 52), but
- the linear programming bound shows that M ≥ 179 097730 485382 466763 358475 272075 270746 626646 991966 962028 395554 430507 849127 640641 078382 459892 462531 880105 047457 276487 957010 177465 406049 917901 560966 128089 033455 258254 007584 468954 494744 013043 770126 452673 441630 415787 945352 424006 715785 946629 131142 326940 562270 465306 937694 549560 546875 / 99 039062 964379 301953 941492 903518 745886 041855 166613 640735 653812 287555 816625 835254 871886 988278 466064 245836 422147 205185 743310 174350 837546 733271 367420 585824 889357 691995 458716 772352 343338 787103 294809 352218 288096 182962 532579 149296 726367 > 569 [i]