MinT - Best Known (11, 15, s)-Nets in Base 7

Best Known (11, 15, s)-Nets in Base 7

Digital (11, 15, 4201)-net over F₇, using

net defined by OOA [i] based on linear OOA(7¹⁵, 4201, F₇, 4, 4) (dual of [(4201, 4), 16789, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(7¹⁵, 4201, F₇, 3, 4) (dual of [(4201, 3), 12588, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(7¹⁵, 8402, F₇, 4) (dual of [8402, 8387, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(7¹⁵, 8403, F₇, 4) (dual of [8403, 8388, 5]-code), using
      - the BCH-code C(I) with length 8403Â | 7⁵âˆ’1, defining interval IÂ =Â {1,3,5,7}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]

Digital (11, 15, 8403)-net over F₇, using

net defined by OOA [i] based on linear OOA(7¹⁵, 8403, F₇, 4, 4) (dual of [(8403, 4), 33597, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(7¹⁵, 8403, F₇, 3, 4) (dual of [(8403, 3), 25194, 5]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7¹⁵, 8403, F₇, 4) (dual of [8403, 8388, 5]-code), using
    - the BCH-code C(I) with length 8403Â | 7⁵âˆ’1, defining interval IÂ =Â {1,3,5,7}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]

There is no (11, 15, 513569)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 4 747571 526769 > 7¹⁵ [i]