MinT - Best Known (71, 114, s)-Nets in Base 16

Best Known (71, 114, s)-Nets in Base 16

(71, 114, 579)-Net over F₁₆ — Constructive and digital

Digital (71, 114, 579)-net over F₁₆, using

16¹ times duplication [i] based on digital (70, 113, 579)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 27, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]
  2. digital (43, 86, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 43, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]

(71, 114, 2063)-Net over F₁₆ — Digital

Digital (71, 114, 2063)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 114, 1744659)-Net in Base 16 — Upper bound on s

There is no (71, 114, 1744660)-net in base 16, because

1 times m-reduction [i] would yield (71, 113, 1744660)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11629 445480 357004 037658 301371 321278 074660 720581 076964 856403 645117 358863 908682 318049 717820 372298 742558 815360 371536 504138 302206 258640 419776 > 16¹¹³ [i]