Best Known (13, 13+39, s)-Nets in Base 5
(13, 13+39, 34)-Net over F5 — Constructive and digital
Digital (13, 52, 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, 13+39, 36)-Net over F5 — Digital
Digital (13, 52, 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, 13+39, 122)-Net in Base 5 — Upper bound on s
There is no (13, 52, 123)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(552, 123, S5, 39), but
- the linear programming bound shows that M ≥ 57743 856481 089955 896348 123518 427885 029218 537008 018960 634769 971488 859577 751844 900870 445493 286951 928979 533477 104268 968105 316162 109375 / 23854 741167 593956 482435 182134 577880 720570 239327 355182 824664 818348 734582 591414 679591 727541 632891 > 552 [i]