MinT - Best Known (200−81, 200, s)-Nets in Base 2

Best Known (200−81, 200, s)-Nets in Base 2

(200−81, 200, 66)-Net over F₂ — Constructive and digital

Digital (119, 200, 66)-net over F₂, using

8 times m-reduction [i] based on digital (119, 208, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 104, 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]

(200−81, 200, 90)-Net over F₂ — Digital

Digital (119, 200, 90)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−81, 200, 439)-Net in Base 2 — Upper bound on s

There is no (119, 200, 440)-net in base 2, because

1 times m-reduction [i] would yield (119, 199, 440)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 837454 354031 500422 439947 994914 480331 361052 603264 168469 876422 > 2¹⁹⁹ [i]