MinT - Best Known (90, 90+39, s)-Nets in Base 2

Best Known (90, 90+39, s)-Nets in Base 2

(90, 90+39, 75)-Net over F₂ — Constructive and digital

Digital (90, 129, 75)-net over F₂, using

trace code for nets [i] based on digital (4, 43, 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]

(90, 90+39, 123)-Net over F₂ — Digital

Digital (90, 129, 123)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+39, 818)-Net in Base 2 — Upper bound on s

There is no (90, 129, 819)-net in base 2, because

1 times m-reduction [i] would yield (90, 128, 819)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 347 262259 602663 420837 723190 498014 004666 > 2¹²⁸ [i]