MinT - Best Known (23−5, 23, s)-Nets in Base 5

Best Known (23−5, 23, s)-Nets in Base 5

Digital (18, 23, 3905)-net over F₅, using

net defined by OOA [i] based on linear OOA(5²³, 3905, F₅, 5, 5) (dual of [(3905, 5), 19502, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(5²³, 7811, F₅, 5) (dual of [7811, 7788, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(5²³, 7812, F₅, 5) (dual of [7812, 7789, 6]-code), using
    - 1 times truncation [i] based on linear OA(5²⁴, 7813, F₅, 6) (dual of [7813, 7789, 7]-code), using
      - the BCH-code C(I) with length 7813Â | 5¹²âˆ’1, defining interval IÂ =Â {−5,−3,−1,…,5}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

Digital (18, 23, 7812)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5²³, 7812, F₅, 5) (dual of [7812, 7789, 6]-code), using
- 1 times truncation [i] based on linear OA(5²⁴, 7813, F₅, 6) (dual of [7813, 7789, 7]-code), using
  - the BCH-code C(I) with length 7813Â | 5¹²âˆ’1, defining interval IÂ =Â {−5,−3,−1,…,5}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

There is no (18, 23, large)-net in base 5, because