MinT - Best Known (80, 80+50, s)-Nets in Base 16

Best Known (80, 80+50, s)-Nets in Base 16

(80, 80+50, 563)-Net over F₁₆ — Constructive and digital

Digital (80, 130, 563)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (5, 30, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]
2. digital (50, 100, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 50, 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]

(80, 80+50, 2019)-Net over F₁₆ — Digital

Digital (80, 130, 2019)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+50, 1238664)-Net in Base 16 — Upper bound on s

There is no (80, 130, 1238665)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 432434 402128 593473 636209 501133 409634 102263 277233 326712 955187 801915 394141 988277 419383 933337 888274 049595 274601 882592 511586 492149 682030 717736 894108 606889 349376 > 16¹³⁰ [i]