MinT - Best Known (232−29, 232, s)-Nets in Base 4

Best Known (232−29, 232, s)-Nets in Base 4

Digital (203, 232, 299593)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²³², 299593, F₄, 29, 29) (dual of [(299593, 29), 8687965, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4²³², 4194303, F₄, 29) (dual of [4194303, 4194071, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²³², 4194304, F₄, 29) (dual of [4194304, 4194072, 30]-code), using
    - an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]

Digital (203, 232, 1110111)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4²³², 1110111, F₄, 3, 29) (dual of [(1110111, 3), 3330101, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4²³², 1398101, F₄, 3, 29) (dual of [(1398101, 3), 4194071, 30]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(4²³², 4194303, F₄, 29) (dual of [4194303, 4194071, 30]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²³², 4194304, F₄, 29) (dual of [4194304, 4194072, 30]-code), using
      - an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]

There is no (203, 232, large)-net in base 4, because

27 times m-reduction [i] would yield (203, 205, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]