MinT - Best Known (53, 86, s)-Nets in Base 2

Best Known (53, 86, s)-Nets in Base 2

(53, 86, 54)-Net over F₂ — Constructive and digital

Digital (53, 86, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 43, 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]

(53, 86, 247)-Net in Base 2 — Upper bound on s

There is no (53, 86, 248)-net in base 2, because

1 times m-reduction [i] would yield (53, 85, 248)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 39 540705 806412 396955 788639 > 2⁸⁵ [i]