Best Known (13, 54, s)-Nets in Base 5
(13, 54, 34)-Net over F5 — Constructive and digital
Digital (13, 54, 34)-net over F5, using
- net from sequence [i] based on digital (13, 33)-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 2 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]
(13, 54, 36)-Net over F5 — Digital
Digital (13, 54, 36)-net over F5, using
- net from sequence [i] based on digital (13, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 13 and N(F) ≥ 36, using
(13, 54, 114)-Net in Base 5 — Upper bound on s
There is no (13, 54, 115)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(554, 115, S5, 41), but
- the linear programming bound shows that M ≥ 202 300469 846898 952332 933038 184302 585147 470724 614419 899337 830505 303412 917979 623777 423821 692225 222873 504932 176812 120958 685848 708575 827112 201661 973929 223137 247390 695847 570896 148681 640625 / 3 374248 089323 892675 901423 922961 840798 946711 745751 437944 996746 192307 662884 044273 216549 080475 454782 162719 647810 263072 294645 323511 987826 919455 260667 > 554 [i]