Best Known (8, 45, s)-Nets in Base 5
(8, 45, 23)-Net over F5 — Constructive and digital
Digital (8, 45, 23)-net over F5, using
- net from sequence [i] based on digital (8, 22)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 7, N(F) = 22, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 7 and N(F) ≥ 22, using an explicitly constructive algebraic function field [i]
(8, 45, 48)-Net over F5 — Upper bound on s (digital)
There is no digital (8, 45, 49)-net over F5, because
- 2 times m-reduction [i] would yield digital (8, 43, 49)-net over F5, but
- extracting embedded orthogonal array [i] would yield linear OA(543, 49, F5, 35) (dual of [49, 6, 36]-code), but
- residual code [i] would yield linear OA(58, 13, F5, 7) (dual of [13, 5, 8]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(543, 49, F5, 35) (dual of [49, 6, 36]-code), but
(8, 45, 50)-Net in Base 5 — Upper bound on s
There is no (8, 45, 51)-net in base 5, because
- 2 times m-reduction [i] would yield (8, 43, 51)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(543, 51, S5, 35), but
- the linear programming bound shows that M ≥ 77449 158197 850920 259952 545166 015625 / 59409 > 543 [i]
- extracting embedded orthogonal array [i] would yield OA(543, 51, S5, 35), but