MinT - Best Known (108−32, 108, s)-Nets in Base 2

Best Known (108−32, 108, s)-Nets in Base 2

(108−32, 108, 75)-Net over F₂ — Constructive and digital

Digital (76, 108, 75)-net over F₂, using

trace code for nets [i] based on digital (4, 36, 25)-net over F₈, using
- net from sequence [i] based on digital (4, 24)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
    - a function field by SÃ©mirat [i]

(108−32, 108, 112)-Net over F₂ — Digital

Digital (76, 108, 112)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−32, 108, 708)-Net in Base 2 — Upper bound on s

There is no (76, 108, 709)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 325 920915 637290 281866 893212 387620 > 2¹⁰⁸ [i]