MinT - Best Known (140, 140+28, s)-Nets in Base 4

Best Known (140, 140+28, s)-Nets in Base 4

Digital (140, 168, 4681)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁶⁸, 4681, F₄, 28, 28) (dual of [(4681, 28), 130900, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(4¹⁶⁸, 65534, F₄, 28) (dual of [65534, 65366, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁶⁸, 65535, F₄, 28) (dual of [65535, 65367, 29]-code), using
    - 1 times truncation [i] based on linear OA(4¹⁶⁹, 65536, F₄, 29) (dual of [65536, 65367, 30]-code), using
      - an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]

Digital (140, 168, 32767)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹⁶⁸, 32767, F₄, 2, 28) (dual of [(32767, 2), 65366, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁶⁸, 65534, F₄, 28) (dual of [65534, 65366, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁶⁸, 65535, F₄, 28) (dual of [65535, 65367, 29]-code), using
    - 1 times truncation [i] based on linear OA(4¹⁶⁹, 65536, F₄, 29) (dual of [65536, 65367, 30]-code), using
      - an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]

There is no (140, 168, large)-net in base 4, because

26 times m-reduction [i] would yield (140, 142, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]