Best Known (85−66, 85, s)-Nets in Base 5
(85−66, 85, 43)-Net over F5 — Constructive and digital
Digital (19, 85, 43)-net over F5, using
- t-expansion [i] based on digital (18, 85, 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
(85−66, 85, 45)-Net over F5 — Digital
Digital (19, 85, 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
(85−66, 85, 107)-Net in Base 5 — Upper bound on s
There is no (19, 85, 108)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(585, 108, S5, 66), but
- the linear programming bound shows that M ≥ 25 451221 799464 996806 965782 377059 969257 028504 419082 537424 401380 121707 916259 765625 / 68 746602 429596 580346 > 585 [i]