MinT - Best Known (79, 79+47, s)-Nets in Base 16

Best Known (79, 79+47, s)-Nets in Base 16

(79, 79+47, 581)-Net over F₁₆ — Constructive and digital

Digital (79, 126, 581)-net over F₁₆, using

16¹ times duplication [i] based on digital (78, 125, 581)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 29, 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 (49, 96, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 48, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(79, 79+47, 2407)-Net over F₁₆ — Digital

Digital (79, 126, 2407)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+47, 2200355)-Net in Base 16 — Upper bound on s

There is no (79, 126, 2200356)-net in base 16, because

1 times m-reduction [i] would yield (79, 125, 2200356)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 273401 818610 330266 740909 899497 622593 665910 799584 010581 722923 224237 452352 002387 748890 440067 414515 482370 930529 106863 707132 644418 009973 306321 890148 363496 > 16¹²⁵ [i]