MinT - Best Known (13−6, 13, s)-Nets in Base 2

Best Known (13−6, 13, s)-Nets in Base 2

(13−6, 13, 23)-Net over F₂ — Constructive and digital

Digital (7, 13, 23)-net over F₂, using

linear code embedding found in a computer search [i]

(13−6, 13, 27)-Net over F₂ — Upper bound on s (digital)

There is no digital (7, 13, 28)-net over F₂, because

extracting embedded orthogonal array [i] would yield linear OA(2¹³, 28, F₂, 6) (dual of [28, 15, 7]-code), but
- adding a parity check bit [i] would yield linear OA(2¹⁴, 29, F₂, 7) (dual of [29, 15, 8]-code), but
  - â€œJaâ€ bound on codes from Brouwerâ€™s database [i]

(13−6, 13, 32)-Net in Base 2 — Upper bound on s

There is no (7, 13, 33)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 8328 > 2¹³ [i]