MinT - Best Known (145, 145+14, s)-Nets in Base 4

Best Known (145, 145+14, s)-Nets in Base 4

Digital (145, 159, 3595113)-net over F₄, using

trace code for nets [i] based on digital (39, 53, 1198371)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁵³, 1198371, F₆₄, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(64⁵³, 8388597, F₆₄, 14) (dual of [8388597, 8388544, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁵³, large, F₆₄, 14) (dual of [large, large−53, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Digital (145, 159, large)-net over F₄, using

4⁴ times duplication [i] based on digital (141, 155, large)-net over F₄, using
- t-expansion [i] based on digital (139, 155, large)-net over F₄, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹⁵⁵, large, F₄, 16) (dual of [large, large−155, 17]-code), using
    - 11 times code embedding in larger space [i] based on linear OA(4¹⁴⁴, large, F₄, 16) (dual of [large, large−144, 17]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

There is no (145, 159, large)-net in base 4, because

12 times m-reduction [i] would yield (145, 147, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]