MinT - Best Known (118−24, 118, s)-Nets in Base 2

Best Known (118−24, 118, s)-Nets in Base 2

(118−24, 118, 196)-Net over F₂ — Constructive and digital

Digital (94, 118, 196)-net over F₂, using

2² 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]

(118−24, 118, 334)-Net over F₂ — Digital

Digital (94, 118, 334)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(118−24, 118, 4807)-Net in Base 2 — Upper bound on s

There is no (94, 118, 4808)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 332766 853021 086243 784074 277341 007144 > 2¹¹⁸ [i]