MinT - Best Known (14, 14+18, s)-Nets in Base 16

Best Known (14, 14+18, s)-Nets in Base 16

Digital (14, 32, 71)-net over F₁₆, using

Digital (14, 32, 102)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(16³², 102, F₁₆, 2, 18) (dual of [(102, 2), 172, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16³², 128, F₁₆, 2, 18) (dual of [(128, 2), 224, 19]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(16³², 256, F₁₆, 18) (dual of [256, 224, 19]-code), using
    - an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 255Â = 16²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]

(14, 32, 104)-net in base 16, using

1 times m-reduction [i] based on (14, 33, 104)-net in base 16, using
- base change [i] based on digital (3, 22, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(14, 32, 113)-net in base 16, using

1 times m-reduction [i] based on (14, 33, 113)-net in base 16, using
- base change [i] based on digital (3, 22, 113)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
      - a curve from the manYPoints database [i]

There is no (14, 32, 5280)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 340 538765 906858 567671 995663 342014 439301 > 16³² [i]