Best Known (67−52, 67, s)-Nets in Base 5
(67−52, 67, 36)-Net over F5 — Constructive and digital
Digital (15, 67, 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]
(67−52, 67, 39)-Net over F5 — Digital
Digital (15, 67, 39)-net over F5, using
- t-expansion [i] based on digital (14, 67, 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
(67−52, 67, 94)-Net in Base 5 — Upper bound on s
There is no (15, 67, 95)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(567, 95, S5, 52), but
- the linear programming bound shows that M ≥ 6 319868 382096 007496 807937 021108 571296 057476 729401 969350 874423 980712 890625 / 89 019237 713775 776017 344912 > 567 [i]