Best Known (89−72, 89, s)-Nets in Base 5
(89−72, 89, 42)-Net over F5 — Constructive and digital
Digital (17, 89, 42)-net over F5, using
- net from sequence [i] based on digital (17, 41)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using
(89−72, 89, 92)-Net in Base 5 — Upper bound on s
There is no (17, 89, 93)-net in base 5, because
- 8 times m-reduction [i] would yield (17, 81, 93)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(581, 93, S5, 64), but
- the linear programming bound shows that M ≥ 615521 895906 900376 246461 033258 317030 458783 847279 846668 243408 203125 / 1347 475701 > 581 [i]
- extracting embedded orthogonal array [i] would yield OA(581, 93, S5, 64), but