MinT - Best Known (120, 120+24, s)-Nets in Base 4

Best Known (120, 120+24, s)-Nets in Base 4

Digital (120, 144, 5461)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁴⁴, 5461, F₄, 24, 24) (dual of [(5461, 24), 130920, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4¹⁴⁴, 65532, F₄, 24) (dual of [65532, 65388, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁴⁴, 65536, F₄, 24) (dual of [65536, 65392, 25]-code), using
    - 1 times truncation [i] based on linear OA(4¹⁴⁵, 65537, F₄, 25) (dual of [65537, 65392, 26]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

Digital (120, 144, 32768)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹⁴⁴, 32768, F₄, 2, 24) (dual of [(32768, 2), 65392, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁴⁴, 65536, F₄, 24) (dual of [65536, 65392, 25]-code), using
  - 1 times truncation [i] based on linear OA(4¹⁴⁵, 65537, F₄, 25) (dual of [65537, 65392, 26]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

There is no (120, 144, large)-net in base 4, because

22 times m-reduction [i] would yield (120, 122, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]