Best Known (15, 15+45, s)-Nets in Base 5
(15, 15+45, 36)-Net over F5 — Constructive and digital
Digital (15, 60, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 4 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(15, 15+45, 39)-Net over F5 — Digital
Digital (15, 60, 39)-net over F5, using
- t-expansion [i] based on digital (14, 60, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(15, 15+45, 133)-Net in Base 5 — Upper bound on s
There is no (15, 60, 134)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(560, 134, S5, 45), but
- the linear programming bound shows that M ≥ 2256 204706 846622 950899 077991 829374 630508 891352 498629 008409 357015 957985 030000 263812 640871 570800 969767 036895 028097 646685 759234 654245 788304 844099 321611 050612 546023 330651 223659 515380 859375 / 2439 468736 362729 613787 952721 532966 568585 829440 233652 051788 837625 933828 693359 667496 275034 097325 062124 561593 329846 621492 401954 669489 004246 596983 > 560 [i]