MinT - Best Known (14, 26, s)-Nets in Base 2

Best Known (14, 26, s)-Nets in Base 2

(14, 26, 26)-Net over F₂ — Constructive and digital

Digital (14, 26, 26)-net over F₂, using

a shift-net [i]

(14, 26, 43)-Net over F₂ — Upper bound on s (digital)

There is no digital (14, 26, 44)-net over F₂, because

extracting embedded orthogonal array [i] would yield linear OA(2²⁶, 44, F₂, 12) (dual of [44, 18, 13]-code), but
- adding a parity check bit [i] would yield linear OA(2²⁷, 45, F₂, 13) (dual of [45, 18, 14]-code), but
  - â€œJaâ€ bound on codes from Brouwerâ€™s database [i]

(14, 26, 52)-Net in Base 2 — Upper bound on s

There is no (14, 26, 53)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 71 653828 > 2²⁶ [i]