MinT - Best Known (117−46, 117, s)-Nets in Base 16

Best Known (117−46, 117, s)-Nets in Base 16

(117−46, 117, 547)-Net over F₁₆ — Constructive and digital

Digital (71, 117, 547)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (2, 25, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]
2. digital (46, 92, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 46, 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]

(117−46, 117, 1610)-Net over F₁₆ — Digital

Digital (71, 117, 1610)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−46, 117, 838811)-Net in Base 16 — Upper bound on s

There is no (71, 117, 838812)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 762 149868 776924 376874 530298 314253 572038 722661 193669 928683 640633 429399 570422 716379 972311 440394 071389 849385 816611 717126 655050 300578 267051 425666 > 16¹¹⁷ [i]