MinT - Best Known (193−79, 193, s)-Nets in Base 2

Best Known (193−79, 193, s)-Nets in Base 2

(193−79, 193, 66)-Net over F₂ — Constructive and digital

Digital (114, 193, 66)-net over F₂, using

5 times m-reduction [i] based on digital (114, 198, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 99, 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]

(193−79, 193, 85)-Net over F₂ — Digital

Digital (114, 193, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−79, 193, 412)-Net in Base 2 — Upper bound on s

There is no (114, 193, 413)-net in base 2, because

1 times m-reduction [i] would yield (114, 192, 413)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6716 105493 774771 772208 386584 577544 677453 882906 595664 041056 > 2¹⁹² [i]