Best Known (69−48, 69, s)-Nets in Base 5
(69−48, 69, 43)-Net over F5 — Constructive and digital
Digital (21, 69, 43)-net over F5, using
- t-expansion [i] based on digital (18, 69, 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
(69−48, 69, 50)-Net over F5 — Digital
Digital (21, 69, 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
(69−48, 69, 226)-Net in Base 5 — Upper bound on s
There is no (21, 69, 227)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(569, 227, S5, 48), but
- the linear programming bound shows that M ≥ 43120 034420 356247 799670 563974 686565 677107 191594 132870 542557 401781 346057 168107 588353 223036 392591 893672 943115 234375 / 25082 081198 310689 525487 009337 454523 517550 452334 855551 408964 686501 > 569 [i]