MinT - Best Known (31, 31+23, s)-Nets in Base 2

Best Known (31, 31+23, s)-Nets in Base 2

(31, 31+23, 30)-Net over F₂ — Constructive and digital

Digital (31, 54, 30)-net over F₂, using

trace code for nets [i] based on digital (4, 27, 15)-net over F₄, using
- net from sequence [i] based on digital (4, 14)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
    - an explicitly constructive algebraic function field [i]

(31, 31+23, 123)-Net in Base 2 — Upper bound on s

There is no (31, 54, 124)-net in base 2, because

1 times m-reduction [i] would yield (31, 53, 124)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 9540 643446 235365 > 2⁵³ [i]