Best Known (5−4, 5, s)-Nets in Base 5
(5−4, 5, 12)-Net over F5 — Constructive and digital
Digital (1, 5, 12)-net over F5, using
(5−4, 5, 12)-Net over F5 — Upper bound on s (digital)
There is no digital (1, 5, 13)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(55, 13, F5, 4) (dual of [13, 8, 5]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
(5−4, 5, 18)-Net in Base 5 — Upper bound on s
There is no (1, 5, 19)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 3193 > 55 [i]
- extracting embedded orthogonal array [i] would yield OA(55, 19, S5, 4), but
- the linear programming bound shows that M ≥ 966875 / 307 > 55 [i]