MinT - Best Known (91, 102, s)-Nets in Base 7

Best Known (91, 102, s)-Nets in Base 7

Digital (91, 102, 3355440)-net over F₇, using

trace code for nets [i] based on digital (40, 51, 1677720)-net over F₄₉, using
- net defined by OOA [i] based on linear OOA(49⁵¹, 1677720, F₄₉, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(49⁵¹, 8388601, F₄₉, 11) (dual of [8388601, 8388550, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(49⁵¹, large, F₄₉, 11) (dual of [large, large−51, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 28247525Â | 49¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Digital (91, 102, large)-net over F₇, using

7⁴ times duplication [i] based on digital (87, 98, large)-net over F₇, using
- t-expansion [i] based on digital (85, 98, large)-net over F₇, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁹⁸, large, F₇, 13) (dual of [large, large−98, 14]-code), using
    - trace code [i] based on linear OA(49⁴⁹, 5764802, F₄₉, 13) (dual of [5764802, 5764753, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 5764802Â | 49⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

There is no (91, 102, large)-net in base 7, because