Best Known (6−3, 6, s)-Nets in Base 27
(6−3, 6, 20496)-Net over F27 — Constructive and digital
Digital (3, 6, 20496)-net over F27, using
- net defined by OOA [i] based on linear OOA(276, 20496, F27, 3, 3) (dual of [(20496, 3), 61482, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(276, 20496, F27, 2, 3) (dual of [(20496, 2), 40986, 4]-NRT-code), using
(6−3, 6, 513971)-Net over F27 — Upper bound on s (digital)
There is no digital (3, 6, 513972)-net over F27, because
- extracting embedded orthogonal array [i] would yield linear OA(276, 513972, F27, 3) (dual of [513972, 513966, 4]-code or 513972-cap in PG(5,27)), but
(6−3, 6, 551880)-Net in Base 27 — Upper bound on s
There is no (3, 6, 551881)-net in base 27, because
- extracting embedded orthogonal array [i] would yield OA(276, 551881, S27, 3), but