Best Known (8−5, 8, s)-Nets in Base 5
(8−5, 8, 33)-Net over F5 — Constructive and digital
Digital (3, 8, 33)-net over F5, using
(8−5, 8, 97)-Net in Base 5 — Upper bound on s
There is no (3, 8, 98)-net in base 5, because
- 1 times m-reduction [i] would yield (3, 7, 98)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 78401 > 57 [i]
- extracting embedded orthogonal array [i] would yield OA(57, 98, S5, 4), but
- the linear programming bound shows that M ≥ 393 471875 / 5011 > 57 [i]