Best Known (22, 142, s)-Nets in Base 5
(22, 142, 51)-Net over F5 — Constructive and digital
Digital (22, 142, 51)-net over F5, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
(22, 142, 115)-Net in Base 5 — Upper bound on s
There is no (22, 142, 116)-net in base 5, because
- 39 times m-reduction [i] would yield (22, 103, 116)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5103, 116, S5, 81), but
- the linear programming bound shows that M ≥ 1237 818286 417009 129589 313695 434643 806752 260386 527808 577739 051543 176174 163818 359375 / 1092 587229 > 5103 [i]
- extracting embedded orthogonal array [i] would yield OA(5103, 116, S5, 81), but