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

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

(55, 55+6, 1048574)-Net over F₂ — Constructive and digital

Digital (55, 61, 1048574)-net over F₂, using

1 times m-reduction [i] based on digital (55, 62, 1048574)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2⁶², 1048574, F₂, 7, 7) (dual of [(1048574, 7), 7339956, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁶², 1048575, F₂, 3, 7) (dual of [(1048575, 3), 3145663, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(55, 55+6, 1048575)-Net over F₂ — Digital

Digital (55, 61, 1048575)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁶¹, 1048575, F₂, 6, 6) (dual of [(1048575, 6), 6291389, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁶¹, 1048575, F₂, 5, 6) (dual of [(1048575, 5), 5242814, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁶¹, 1048575, F₂, 2, 6) (dual of [(1048575, 2), 2097089, 7]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(55, 55+6, 2400635)-Net in Base 2 — Upper bound on s

There is no (55, 61, 2400636)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 305843 691556 088643 > 2⁶¹ [i]