MinT - Best Known (224−97, 224, s)-Nets in Base 2

Best Known (224−97, 224, s)-Nets in Base 2

(224−97, 224, 66)-Net over F₂ — Constructive and digital

Digital (127, 224, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 112, 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]

(224−97, 224, 85)-Net over F₂ — Digital

Digital (127, 224, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−97, 224, 402)-Net in Base 2 — Upper bound on s

There is no (127, 224, 403)-net in base 2, because

1 times m-reduction [i] would yield (127, 223, 403)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14 536635 997296 913775 081504 288190 391088 905200 704409 492016 554865 315564 > 2²²³ [i]