MinT - Best Known (250−46, 250, s)-Nets in Base 2

Best Known (250−46, 250, s)-Nets in Base 2

(250−46, 250, 320)-Net over F₂ — Constructive and digital

Digital (204, 250, 320)-net over F₂, using

t-expansion [i] based on digital (203, 250, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 50, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(250−46, 250, 816)-Net over F₂ — Digital

Digital (204, 250, 816)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−46, 250, 17606)-Net in Base 2 — Upper bound on s

There is no (204, 250, 17607)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1809 348575 229638 186276 761361 579508 591714 114077 446353 832062 032517 689838 014840 > 2²⁵⁰ [i]