MinT - Best Known (96−31, 96, s)-Nets in Base 2

Best Known (96−31, 96, s)-Nets in Base 2

(96−31, 96, 66)-Net over F₂ — Constructive and digital

Digital (65, 96, 66)-net over F₂, using

4 times m-reduction [i] based on digital (65, 100, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 50, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(96−31, 96, 84)-Net over F₂ — Digital

Digital (65, 96, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−31, 96, 496)-Net in Base 2 — Upper bound on s

There is no (65, 96, 497)-net in base 2, because

1 times m-reduction [i] would yield (65, 95, 497)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 40348 049980 731669 673230 729216 > 2⁹⁵ [i]