MinT - Best Known (116−24, 116, s)-Nets in Base 2

Best Known (116−24, 116, s)-Nets in Base 2

(116−24, 116, 196)-Net over F₂ — Constructive and digital

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]

(116−24, 116, 312)-Net over F₂ — Digital

Digital (92, 116, 312)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−24, 116, 4281)-Net in Base 2 — Upper bound on s

There is no (92, 116, 4282)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 83298 976952 529339 397053 171663 541284 > 2¹¹⁶ [i]