Best Known (37−30, 37, s)-Nets in Base 5
(37−30, 37, 22)-Net over F5 — Constructive and digital
Digital (7, 37, 22)-net over F5, using
- net from sequence [i] based on digital (7, 21)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 7 and N(F) ≥ 22, using
(37−30, 37, 42)-Net over F5 — Upper bound on s (digital)
There is no digital (7, 37, 43)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(537, 43, F5, 30) (dual of [43, 6, 31]-code), but
- residual code [i] would yield linear OA(57, 12, F5, 6) (dual of [12, 5, 7]-code), but
(37−30, 37, 49)-Net in Base 5 — Upper bound on s
There is no (7, 37, 50)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(537, 50, S5, 30), but
- the linear programming bound shows that M ≥ 1901 298674 056306 481361 389160 156250 / 18 732649 > 537 [i]