MinT - Best Known (85−11, 85, s)-Nets in Base 5

Best Known (85−11, 85, s)-Nets in Base 5

Digital (74, 85, 1677720)-net over F₅, using

5⁴ times duplication [i] based on digital (70, 81, 1677720)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5⁸¹, 1677720, F₅, 11, 11) (dual of [(1677720, 11), 18454839, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(5⁸¹, 8388601, F₅, 11) (dual of [8388601, 8388520, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁸¹, large, F₅, 11) (dual of [large, large−81, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Digital (74, 85, 4194303)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(5⁸⁵, 4194303, F₅, 2, 11) (dual of [(4194303, 2), 8388521, 12]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(5⁸¹, 4194301, F₅, 2, 11) (dual of [(4194301, 2), 8388521, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(5⁸¹, 8388602, F₅, 11) (dual of [8388602, 8388521, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁸¹, large, F₅, 11) (dual of [large, large−81, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

There is no (74, 85, large)-net in base 5, because