Best Known (13, 13+48, s)-Nets in Base 5
(13, 13+48, 34)-Net over F5 — Constructive and digital
Digital (13, 61, 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+48, 36)-Net over F5 — Digital
Digital (13, 61, 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+48, 79)-Net in Base 5 — Upper bound on s
There is no (13, 61, 80)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(561, 80, S5, 48), but
- the linear programming bound shows that M ≥ 46 179017 708825 216559 365145 485571 702010 929584 503173 828125 / 8 381370 687228 > 561 [i]