MinT - Best Known (91−36, 91, s)-Nets in Base 16

Best Known (91−36, 91, s)-Nets in Base 16

(91−36, 91, 538)-Net over F₁₆ — Constructive and digital

Digital (55, 91, 538)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (1, 19, 24)-net over F₁₆, using
  - net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
2. digital (36, 72, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 36, 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]

(91−36, 91, 1270)-Net over F₁₆ — Digital

Digital (55, 91, 1270)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(91−36, 91, 615924)-Net in Base 16 — Upper bound on s

There is no (55, 91, 615925)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 37 577313 898829 891547 237366 221531 777269 052620 688380 316336 526379 747757 844980 465339 279410 065314 142573 683548 691626 > 16⁹¹ [i]