MinT - Best Known (8, 8+6, s)-Nets in Base 2

Best Known (8, 8+6, s)-Nets in Base 2

(8, 8+6, 26)-Net over F₂ — Constructive and digital

Digital (8, 14, 26)-net over F₂, using

linear code embedding found in a computer search [i]

(8, 8+6, 40)-Net over F₂ — Upper bound on s (digital)

There is no digital (8, 14, 41)-net over F₂, because

extracting embedded orthogonal array [i] would yield linear OA(2¹⁴, 41, F₂, 6) (dual of [41, 27, 7]-code), but
- adding a parity check bit [i] would yield linear OA(2¹⁵, 42, F₂, 7) (dual of [42, 27, 8]-code), but
  - â€œJaâ€ bound on codes from Brouwerâ€™s database [i]

(8, 8+6, 42)-Net in Base 2 — Upper bound on s

There is no (8, 14, 43)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 17158 > 2¹⁴ [i]