MinT - Best Known (117−24, 117, s)-Nets in Base 2

Best Known (117−24, 117, s)-Nets in Base 2

(117−24, 117, 196)-Net over F₂ — Constructive and digital

Digital (93, 117, 196)-net over F₂, using

2¹ times duplication [i] based on digital (92, 116, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 29, 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]

(117−24, 117, 323)-Net over F₂ — Digital

Digital (93, 117, 323)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−24, 117, 4536)-Net in Base 2 — Upper bound on s

There is no (93, 117, 4537)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 166309 449035 815541 731123 453568 188564 > 2¹¹⁷ [i]