MinT - Best Known (48, 80, s)-Nets in Base 16

Best Known (48, 80, s)-Nets in Base 16

(48, 80, 531)-Net over F₁₆ — Constructive and digital

Digital (48, 80, 531)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 16, 17)-net over F₁₆, using
  - net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
      - the rational function field F₁₆(x) [i]
    - Niederreiter sequence [i]
2. digital (32, 64, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 32, 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]

(48, 80, 1076)-Net over F₁₆ — Digital

Digital (48, 80, 1076)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 80, 475378)-Net in Base 16 — Upper bound on s

There is no (48, 80, 475379)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 136021 667900 815978 708392 274616 536696 752784 940756 584328 938547 035406 078567 838915 594943 020789 517211 > 16⁸⁰ [i]