Best Known (68−53, 68, s)-Nets in Base 5
(68−53, 68, 36)-Net over F5 — Constructive and digital
Digital (15, 68, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 4 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(68−53, 68, 39)-Net over F5 — Digital
Digital (15, 68, 39)-net over F5, using
- t-expansion [i] based on digital (14, 68, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(68−53, 68, 91)-Net in Base 5 — Upper bound on s
There is no (15, 68, 92)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(568, 92, S5, 53), but
- the linear programming bound shows that M ≥ 27259 079834 587745 088119 066505 516485 676707 816310 226917 266845 703125 / 74895 994142 880768 > 568 [i]