MinT - Best Known (60, 72, s)-Nets in Base 4

Best Known (60, 72, s)-Nets in Base 4

Digital (60, 72, 10922)-net over F₄, using

net defined by OOA [i] based on linear OOA(4⁷², 10922, F₄, 12, 12) (dual of [(10922, 12), 130992, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(4⁷², 65532, F₄, 12) (dual of [65532, 65460, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁷², 65535, F₄, 12) (dual of [65535, 65463, 13]-code), using
    - 1 times truncation [i] based on linear OA(4⁷³, 65536, F₄, 13) (dual of [65536, 65463, 14]-code), using
      - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Digital (60, 72, 32767)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4⁷², 32767, F₄, 2, 12) (dual of [(32767, 2), 65462, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4⁷², 65534, F₄, 12) (dual of [65534, 65462, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁷², 65535, F₄, 12) (dual of [65535, 65463, 13]-code), using
    - 1 times truncation [i] based on linear OA(4⁷³, 65536, F₄, 13) (dual of [65536, 65463, 14]-code), using
      - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

There is no (60, 72, large)-net in base 4, because

10 times m-reduction [i] would yield (60, 62, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]