MinT - Best Known (225−95, 225, s)-Nets in Base 2

Best Known (225−95, 225, s)-Nets in Base 2

(225−95, 225, 66)-Net over F₂ — Constructive and digital

Digital (130, 225, 66)-net over F₂, using

5 times m-reduction [i] based on digital (130, 230, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 115, 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]

(225−95, 225, 90)-Net over F₂ — Digital

Digital (130, 225, 90)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−95, 225, 433)-Net in Base 2 — Upper bound on s

There is no (130, 225, 434)-net in base 2, because

1 times m-reduction [i] would yield (130, 224, 434)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27 043127 604265 325348 320109 550308 993556 992403 971113 743277 692700 836408 > 2²²⁴ [i]