MinT - Best Known (38, 38+12, s)-Nets in Base 7

Best Known (38, 38+12, s)-Nets in Base 7

Digital (38, 50, 1400)-net over F₇, using

net defined by OOA [i] based on linear OOA(7⁵⁰, 1400, F₇, 12, 12) (dual of [(1400, 12), 16750, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(7⁵⁰, 8400, F₇, 12) (dual of [8400, 8350, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁵⁰, 8403, F₇, 12) (dual of [8403, 8353, 13]-code), using
    - the BCH-code C(I) with length 8403Â | 7⁵âˆ’1, defining interval IÂ =Â {1,3,5,…,23}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Digital (38, 50, 8403)-net over F₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁵⁰, 8403, F₇, 12) (dual of [8403, 8353, 13]-code), using
- the BCH-code C(I) with length 8403Â | 7⁵âˆ’1, defining interval IÂ =Â {1,3,5,…,23}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

There is no (38, 50, 5502427)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1 798466 698449 890285 860369 922378 342334 343381 > 7⁵⁰ [i]