MinT - Best Known (196−79, 196, s)-Nets in Base 2

Best Known (196−79, 196, s)-Nets in Base 2

(196−79, 196, 66)-Net over F₂ — Constructive and digital

Digital (117, 196, 66)-net over F₂, using

8 times m-reduction [i] based on digital (117, 204, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 102, 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]

(196−79, 196, 89)-Net over F₂ — Digital

Digital (117, 196, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−79, 196, 437)-Net in Base 2 — Upper bound on s

There is no (117, 196, 438)-net in base 2, because

1 times m-reduction [i] would yield (117, 195, 438)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 51733 204458 746549 690113 415802 442421 046244 410851 381689 817388 > 2¹⁹⁵ [i]