MinT - Best Known (208−58, 208, s)-Nets in Base 2

Best Known (208−58, 208, s)-Nets in Base 2

(208−58, 208, 144)-Net over F₂ — Constructive and digital

Digital (150, 208, 144)-net over F₂, using

2¹ times duplication [i] based on digital (149, 207, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 69, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(208−58, 208, 220)-Net over F₂ — Digital

Digital (150, 208, 220)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−58, 208, 1641)-Net in Base 2 — Upper bound on s

There is no (150, 208, 1642)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 417 980362 576665 928281 961826 030706 528141 965559 639229 669736 104136 > 2²⁰⁸ [i]