MinT - Best Known (82, 82+10, s)-Nets in Base 7

Best Known (82, 82+10, s)-Nets in Base 7

Digital (82, 92, 3355440)-net over F₇, using

trace code for nets [i] based on digital (36, 46, 1677720)-net over F₄₉, using
- net defined by OOA [i] based on linear OOA(49⁴⁶, 1677720, F₄₉, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(49⁴⁶, 8388600, F₄₉, 10) (dual of [8388600, 8388554, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(49⁴⁶, large, F₄₉, 10) (dual of [large, large−46, 11]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 25679568Â | 49⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Digital (82, 92, large)-net over F₇, using

7² times duplication [i] based on digital (80, 90, large)-net over F₇, using
- t-expansion [i] based on digital (78, 90, large)-net over F₇, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁹⁰, large, F₇, 12) (dual of [large, large−90, 13]-code), using
    - trace code [i] based on linear OA(49⁴⁵, 5764801, F₄₉, 12) (dual of [5764801, 5764756, 13]-code), using
      - an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

There is no (82, 92, large)-net in base 7, because