Best Known (93−72, 93, s)-Nets in Base 5
(93−72, 93, 43)-Net over F5 — Constructive and digital
Digital (21, 93, 43)-net over F5, using
- t-expansion [i] based on digital (18, 93, 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
(93−72, 93, 50)-Net over F5 — Digital
Digital (21, 93, 50)-net over F5, using
- net from sequence [i] based on digital (21, 49)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 21 and N(F) ≥ 50, using
(93−72, 93, 115)-Net in Base 5 — Upper bound on s
There is no (21, 93, 116)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(593, 116, S5, 72), but
- the linear programming bound shows that M ≥ 10788 210448 206637 685640 916232 664629 210817 597293 470271 324622 444808 483123 779296 875000 / 92115 440265 879693 > 593 [i]