MinT - Best Known (19, 26, s)-Nets in Base 2

Best Known (19, 26, s)-Nets in Base 2

(19, 26, 254)-Net over F₂ — Constructive and digital

Digital (19, 26, 254)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²⁶, 254, F₂, 7, 7) (dual of [(254, 7), 1752, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2²⁶, 255, F₂, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]

(19, 26, 255)-Net over F₂ — Digital

Digital (19, 26, 255)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²⁶, 255, F₂, 7, 7) (dual of [(255, 7), 1759, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(2²⁶, 255, F₂, 6, 7) (dual of [(255, 6), 1504, 8]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁶, 255, F₂, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(19, 26, 582)-Net in Base 2 — Upper bound on s

There is no (19, 26, 583)-net in base 2, because

1 times m-reduction [i] would yield (19, 25, 583)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 33 708478 > 2²⁵ [i]