MinT - Best Known (44, 44+16, s)-Nets in Base 16

Best Known (44, 44+16, s)-Nets in Base 16

Digital (44, 60, 8191)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16⁶⁰, 8191, F₁₆, 16, 16) (dual of [(8191, 16), 130996, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(16⁶⁰, 65528, F₁₆, 16) (dual of [65528, 65468, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁶⁰, 65535, F₁₆, 16) (dual of [65535, 65475, 17]-code), using
    - 1 times truncation [i] based on linear OA(16⁶¹, 65536, F₁₆, 17) (dual of [65536, 65475, 18]-code), using
      - an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 16⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Digital (44, 60, 47842)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁶⁰, 47842, F₁₆, 16) (dual of [47842, 47782, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁶⁰, 65535, F₁₆, 16) (dual of [65535, 65475, 17]-code), using
  - 1 times truncation [i] based on linear OA(16⁶¹, 65536, F₁₆, 17) (dual of [65536, 65475, 18]-code), using
    - an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 16⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

There is no (44, 60, large)-net in base 16, because

14 times m-reduction [i] would yield (44, 46, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]