MinT - Best Known (252−28, 252, s)-Nets in Base 4

Best Known (252−28, 252, s)-Nets in Base 4

Digital (224, 252, 599185)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²⁵², 599185, F₄, 28, 28) (dual of [(599185, 28), 16776928, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(4²⁵², 8388590, F₄, 28) (dual of [8388590, 8388338, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²⁵², large, F₄, 28) (dual of [large, large−252, 29]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]

Digital (224, 252, 3557149)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4²⁵², 3557149, F₄, 2, 28) (dual of [(3557149, 2), 7114046, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4²⁵², 4194301, F₄, 2, 28) (dual of [(4194301, 2), 8388350, 29]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²⁵², 8388602, F₄, 28) (dual of [8388602, 8388350, 29]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²⁵², large, F₄, 28) (dual of [large, large−252, 29]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]

There is no (224, 252, large)-net in base 4, because

26 times m-reduction [i] would yield (224, 226, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]