MinT - Best Known (92, 92+14, s)-Nets in Base 8

Best Known (92, 92+14, s)-Nets in Base 8

Digital (92, 106, 2396742)-net over F₈, 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 (92, 106, large)-net over F₈, using

8¹ times duplication [i] based on digital (91, 105, large)-net over F₈, using
- t-expansion [i] based on digital (90, 105, large)-net over F₈, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8¹⁰⁵, large, F₈, 15) (dual of [large, large−105, 16]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 8⁸âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

There is no (92, 106, large)-net in base 8, because

12 times m-reduction [i] would yield (92, 94, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]