MinT - Best Known (82, 82+28, s)-Nets in Base 16

Best Known (82, 82+28, s)-Nets in Base 16

Digital (82, 110, 9362)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16¹¹⁰, 9362, F₁₆, 28, 28) (dual of [(9362, 28), 262026, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(16¹¹⁰, 131068, F₁₆, 28) (dual of [131068, 130958, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹¹⁰, 131072, F₁₆, 28) (dual of [131072, 130962, 29]-code), using
    - trace code [i] based on linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using
      - an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]

Digital (82, 110, 78554)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16¹¹⁰, 78554, F₁₆, 28) (dual of [78554, 78444, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹¹⁰, 131072, F₁₆, 28) (dual of [131072, 130962, 29]-code), using
  - trace code [i] based on linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using
    - an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]

There is no (82, 110, large)-net in base 16, because

26 times m-reduction [i] would yield (82, 84, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]