Best Known (13, 13+46, s)-Nets in Base 5
(13, 13+46, 34)-Net over F5 — Constructive and digital
Digital (13, 59, 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+46, 36)-Net over F5 — Digital
Digital (13, 59, 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+46, 87)-Net in Base 5 — Upper bound on s
There is no (13, 59, 88)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(559, 88, S5, 46), but
- the linear programming bound shows that M ≥ 1 201888 190975 048522 048866 488087 792703 254308 435134 589672 088623 046875 / 6 290413 958079 688593 881088 > 559 [i]