MinT - Best Known (165−44, 165, s)-Nets in Base 2

Best Known (165−44, 165, s)-Nets in Base 2

(165−44, 165, 144)-Net over F₂ — Constructive and digital

Digital (121, 165, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 55, 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]

(165−44, 165, 203)-Net over F₂ — Digital

Digital (121, 165, 203)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−44, 165, 1606)-Net in Base 2 — Upper bound on s

There is no (121, 165, 1607)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 46 901867 819489 847341 970242 974991 651011 235172 695004 > 2¹⁶⁵ [i]