MinT - Best Known (125−46, 125, s)-Nets in Base 16

Best Known (125−46, 125, s)-Nets in Base 16

(125−46, 125, 583)-Net over F₁₆ — Constructive and digital

Digital (79, 125, 583)-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 (50, 96, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 48, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(125−46, 125, 2622)-Net over F₁₆ — Digital

Digital (79, 125, 2622)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−46, 125, 2200355)-Net in Base 16 — Upper bound on s

There is no (79, 125, 2200356)-net in base 16, because

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]