MinT - Best Known (25, 31, s)-Nets in Base 2

Best Known (25, 31, s)-Nets in Base 2

(25, 31, 1022)-Net over F₂ — Constructive and digital

Digital (25, 31, 1022)-net over F₂, using

1 times m-reduction [i] based on digital (25, 32, 1022)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2³², 1022, F₂, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2³², 1023, F₂, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(25, 31, 1023)-Net over F₂ — Digital

Digital (25, 31, 1023)-net over F₂, using

net defined by OOA [i] based on linear OOA(2³¹, 1023, F₂, 6, 6) (dual of [(1023, 6), 6107, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2³¹, 1023, F₂, 5, 6) (dual of [(1023, 5), 5084, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2³¹, 1023, F₂, 2, 6) (dual of [(1023, 2), 2015, 7]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(25, 31, 2340)-Net in Base 2 — Upper bound on s

There is no (25, 31, 2341)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2149 194848 > 2³¹ [i]