MinT - Best Known (30, 30+20, s)-Nets in Base 2

Best Known (30, 30+20, s)-Nets in Base 2

(30, 30+20, 34)-Net over F₂ — Constructive and digital

Digital (30, 50, 34)-net over F₂, using

trace code for nets [i] based on digital (5, 25, 17)-net over F₄, using
- net from sequence [i] based on digital (5, 16)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]

(30, 30+20, 131)-Net in Base 2 — Upper bound on s

There is no (30, 50, 132)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1203 299754 367888 > 2⁵⁰ [i]