MinT - Best Known (203, 203+28, s)-Nets in Base 4

Best Known (203, 203+28, s)-Nets in Base 4

Digital (203, 231, 299593)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²³¹, 299593, F₄, 28, 28) (dual of [(299593, 28), 8388373, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(4²³¹, 4194302, F₄, 28) (dual of [4194302, 4194071, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²³¹, 4194303, F₄, 28) (dual of [4194303, 4194072, 29]-code), using
    - 1 times truncation [i] 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, 231, 1398101)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4²³¹, 1398101, F₄, 3, 28) (dual of [(1398101, 3), 4194072, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4²³¹, 4194303, F₄, 28) (dual of [4194303, 4194072, 29]-code), using
  - 1 times truncation [i] 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, 231, large)-net in base 4, because

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