MinT - Best Known (105−31, 105, s)-Nets in Base 2

Best Known (105−31, 105, s)-Nets in Base 2

(105−31, 105, 75)-Net over F₂ — Constructive and digital

Digital (74, 105, 75)-net over F₂, using

trace code for nets [i] based on digital (4, 35, 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]

(105−31, 105, 111)-Net over F₂ — Digital

Digital (74, 105, 111)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−31, 105, 763)-Net in Base 2 — Upper bound on s

There is no (74, 105, 764)-net in base 2, because

1 times m-reduction [i] would yield (74, 104, 764)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20 538102 110756 716866 397799 439668 > 2¹⁰⁴ [i]