MinT - Best Known (66, 66+12, s)-Nets in Base 2

Best Known (66, 66+12, s)-Nets in Base 2

Digital (66, 78, 1365)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁷⁸, 1365, F₂, 12, 12) (dual of [(1365, 12), 16302, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2⁷⁸, 8190, F₂, 12) (dual of [8190, 8112, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁷⁸, 8191, F₂, 12) (dual of [8191, 8113, 13]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Digital (66, 78, 2488)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁷⁸, 2488, F₂, 3, 12) (dual of [(2488, 3), 7386, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁷⁸, 2730, F₂, 3, 12) (dual of [(2730, 3), 8112, 13]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁷⁸, 8190, F₂, 12) (dual of [8190, 8112, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(2⁷⁸, 8191, F₂, 12) (dual of [8191, 8113, 13]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

There is no (66, 78, 24517)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 302255 761358 084034 092860 > 2⁷⁸ [i]