MinT - Best Known (116, 132, s)-Nets in Base 4

Best Known (116, 132, s)-Nets in Base 4

Digital (116, 132, 524288)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹³², 524288, F₄, 16, 16) (dual of [(524288, 16), 8388476, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4¹³², 4194304, F₄, 16) (dual of [4194304, 4194172, 17]-code), using
  - 1 times truncation [i] based on linear OA(4¹³³, 4194305, F₄, 17) (dual of [4194305, 4194172, 18]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 4²²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Digital (116, 132, 1980992)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹³², 1980992, F₄, 2, 16) (dual of [(1980992, 2), 3961852, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹³², 2097152, F₄, 2, 16) (dual of [(2097152, 2), 4194172, 17]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹³², 4194304, F₄, 16) (dual of [4194304, 4194172, 17]-code), using
    - 1 times truncation [i] based on linear OA(4¹³³, 4194305, F₄, 17) (dual of [4194305, 4194172, 18]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 4²²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

There is no (116, 132, large)-net in base 4, because

14 times m-reduction [i] would yield (116, 118, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]