Best Known (14, 14+39, s)-Nets in Base 5
(14, 14+39, 35)-Net over F5 — Constructive and digital
Digital (14, 53, 35)-net over F5, using
- net from sequence [i] based on digital (14, 34)-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 3 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]
(14, 14+39, 39)-Net over F5 — Digital
Digital (14, 53, 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
(14, 14+39, 139)-Net in Base 5 — Upper bound on s
There is no (14, 53, 140)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(553, 140, S5, 39), but
- the linear programming bound shows that M ≥ 15797 706962 756455 435925 942967 079189 858744 896047 398586 831387 374586 098383 722543 303520 069457 590579 986572 265625 / 1404 451882 069680 664381 950768 964914 157064 632742 400081 090096 232135 809289 > 553 [i]