Best Known (37−28, 37, s)-Nets in Base 5
(37−28, 37, 26)-Net over F5 — Constructive and digital
Digital (9, 37, 26)-net over F5, using
- net from sequence [i] based on digital (9, 25)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 9 and N(F) ≥ 26, using
(37−28, 37, 96)-Net in Base 5 — Upper bound on s
There is no (9, 37, 97)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 76 048097 408160 563352 355305 > 537 [i]
- extracting embedded orthogonal array [i] would yield OA(537, 97, S5, 28), but
- the linear programming bound shows that M ≥ 2617 602475 583204 249825 292528 677407 558076 083660 125732 421875 / 33 613625 416773 168534 885172 294721 > 537 [i]