MinT - Best Known (80−30, 80, s)-Nets in Base 2

Best Known (80−30, 80, s)-Nets in Base 2

(80−30, 80, 54)-Net over F₂ — Constructive and digital

Digital (50, 80, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 40, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(80−30, 80, 237)-Net in Base 2 — Upper bound on s

There is no (50, 80, 238)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 224083 489080 943709 929948 > 2⁸⁰ [i]