MinT - Best Known (96, 96+13, s)-Nets in Base 4

Best Known (96, 96+13, s)-Nets in Base 4

Digital (96, 109, 1398100)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁰⁹, 1398100, F₄, 13, 13) (dual of [(1398100, 13), 18175191, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4¹⁰⁹, 8388601, F₄, 13) (dual of [8388601, 8388492, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁰⁹, large, F₄, 13) (dual of [large, large−109, 14]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

Digital (96, 109, 4177305)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹⁰⁹, 4177305, F₄, 2, 13) (dual of [(4177305, 2), 8354501, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁰⁹, 4194301, F₄, 2, 13) (dual of [(4194301, 2), 8388493, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁰⁹, 8388602, F₄, 13) (dual of [8388602, 8388493, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁰⁹, large, F₄, 13) (dual of [large, large−109, 14]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

There is no (96, 109, large)-net in base 4, because

11 times m-reduction [i] would yield (96, 98, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]