MinT - Best Known (55−6, 55, s)-Nets in Base 2

Best Known (55−6, 55, s)-Nets in Base 2

(55−6, 55, 262142)-Net over F₂ — Constructive and digital

Digital (49, 55, 262142)-net over F₂, using

1 times m-reduction [i] based on digital (49, 56, 262142)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2⁵⁶, 262142, F₂, 7, 7) (dual of [(262142, 7), 1834938, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁵⁶, 262143, F₂, 3, 7) (dual of [(262143, 3), 786373, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(55−6, 55, 262143)-Net over F₂ — Digital

Digital (49, 55, 262143)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁵⁵, 262143, F₂, 6, 6) (dual of [(262143, 6), 1572803, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁵⁵, 262143, F₂, 5, 6) (dual of [(262143, 5), 1310660, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁵⁵, 262143, F₂, 2, 6) (dual of [(262143, 2), 524231, 7]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(55−6, 55, 600155)-Net in Base 2 — Upper bound on s

There is no (49, 55, 600156)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 36028 807678 782163 > 2⁵⁵ [i]