Best Known (19, 19+63, s)-Nets in Base 5
(19, 19+63, 43)-Net over F5 — Constructive and digital
Digital (19, 82, 43)-net over F5, using
- t-expansion [i] based on digital (18, 82, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
(19, 19+63, 45)-Net over F5 — Digital
Digital (19, 82, 45)-net over F5, using
- net from sequence [i] based on digital (19, 44)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 19 and N(F) ≥ 45, using
(19, 19+63, 115)-Net in Base 5 — Upper bound on s
There is no (19, 82, 116)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(582, 116, S5, 63), but
- the linear programming bound shows that M ≥ 41902 297568 579850 065184 823392 203241 249066 487136 669401 092348 152815 247885 882854 461669 921875 / 18 952166 879374 328236 271624 013024 > 582 [i]