MinT - Best Known (88, 88+30, s)-Nets in Base 16

Best Known (88, 88+30, s)-Nets in Base 16

Digital (88, 118, 8738)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16¹¹⁸, 8738, F₁₆, 30, 30) (dual of [(8738, 30), 262022, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(16¹¹⁸, 131070, F₁₆, 30) (dual of [131070, 130952, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹¹⁸, 131072, F₁₆, 30) (dual of [131072, 130954, 31]-code), using
    - trace code [i] based on linear OA(256⁵⁹, 65536, F₂₅₆, 30) (dual of [65536, 65477, 31]-code), using
      - an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]

Digital (88, 118, 80972)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16¹¹⁸, 80972, F₁₆, 30) (dual of [80972, 80854, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹¹⁸, 131072, F₁₆, 30) (dual of [131072, 130954, 31]-code), using
  - trace code [i] based on linear OA(256⁵⁹, 65536, F₂₅₆, 30) (dual of [65536, 65477, 31]-code), using
    - an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]

There is no (88, 118, large)-net in base 16, because

28 times m-reduction [i] would yield (88, 90, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]