MinT - Best Known (250−55, 250, s)-Nets in Base 2

Best Known (250−55, 250, s)-Nets in Base 2

(250−55, 250, 260)-Net over F₂ — Constructive and digital

Digital (195, 250, 260)-net over F₂, using

2 times m-reduction [i] based on digital (195, 252, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 63, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(250−55, 250, 475)-Net over F₂ — Digital

Digital (195, 250, 475)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−55, 250, 6484)-Net in Base 2 — Upper bound on s

There is no (195, 250, 6485)-net in base 2, because

1 times m-reduction [i] would yield (195, 249, 6485)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 904 669975 585422 583567 826822 341059 102344 305058 736015 238604 047856 091955 586816 > 2²⁴⁹ [i]