MinT - Best Known (76, 76+26, s)-Nets in Base 16

Best Known (76, 76+26, s)-Nets in Base 16

Digital (76, 102, 10082)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16¹⁰², 10082, F₁₆, 26, 26) (dual of [(10082, 26), 262030, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(16¹⁰², 131066, F₁₆, 26) (dual of [131066, 130964, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁰², 131072, F₁₆, 26) (dual of [131072, 130970, 27]-code), using
    - trace code [i] based on linear OA(256⁵¹, 65536, F₂₅₆, 26) (dual of [65536, 65485, 27]-code), using
      - an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

Digital (76, 102, 76302)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16¹⁰², 76302, F₁₆, 26) (dual of [76302, 76200, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹⁰², 131072, F₁₆, 26) (dual of [131072, 130970, 27]-code), using
  - trace code [i] based on linear OA(256⁵¹, 65536, F₂₅₆, 26) (dual of [65536, 65485, 27]-code), using
    - an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

There is no (76, 102, large)-net in base 16, because

24 times m-reduction [i] would yield (76, 78, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]