MinT - Best Known (4, 12, s)-Nets in Base 3

Best Known (4, 12, s)-Nets in Base 3

(4, 12, 14)-Net over F₃ — Constructive and digital

Digital (4, 12, 14)-net over F₃, using

linear code embedding found in a computer search [i]

(4, 12, 24)-Net over F₃ — Upper bound on s (digital)

There is no digital (4, 12, 25)-net over F₃, because

extracting embedded orthogonal array [i] would yield linear OA(3¹², 25, F₃, 8) (dual of [25, 13, 9]-code), but
- â€œLPâ€ bound on codes from Brouwerâ€™s database [i]

(4, 12, 26)-Net in Base 3 — Upper bound on s

There is no (4, 12, 27)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 564697 > 3¹² [i]