Best Known (89−68, 89, s)-Nets in Base 5
(89−68, 89, 43)-Net over F5 — Constructive and digital
Digital (21, 89, 43)-net over F5, using
- t-expansion [i] based on digital (18, 89, 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
(89−68, 89, 50)-Net over F5 — Digital
Digital (21, 89, 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
(89−68, 89, 127)-Net in Base 5 — Upper bound on s
There is no (21, 89, 128)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(589, 128, S5, 68), but
- the linear programming bound shows that M ≥ 469 692866 807591 375427 341890 531758 805523 348308 690396 565238 771298 123054 975803 825072 944164 276123 046875 / 2 848778 646702 863039 588267 347915 991007 > 589 [i]