MinT - Best Known (15−8, 15, s)-Nets in Base 2

Best Known (15−8, 15, s)-Nets in Base 2

(15−8, 15, 16)-Net over F₂ — Constructive and digital

Digital (7, 15, 16)-net over F₂, using

linear code embedding found in a computer search [i]

(15−8, 15, 20)-Net over F₂ — Upper bound on s (digital)

There is no digital (7, 15, 21)-net over F₂, because

extracting embedded orthogonal array [i] would yield linear OA(2¹⁵, 21, F₂, 8) (dual of [21, 6, 9]-code), but
- residual code [i] would yield linear OA(2⁷, 12, F₂, 4) (dual of [12, 5, 5]-code), but
  - bound by Fontaine and Peterson [i]

(15−8, 15, 24)-Net in Base 2 — Upper bound on s

There is no (7, 15, 25)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 34226 > 2¹⁵ [i]