MinT - Best Known (207−58, 207, s)-Nets in Base 2

Best Known (207−58, 207, s)-Nets in Base 2

(207−58, 207, 144)-Net over F₂ — Constructive and digital

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]

(207−58, 207, 216)-Net over F₂ — Digital

Digital (149, 207, 216)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−58, 207, 1601)-Net in Base 2 — Upper bound on s

There is no (149, 207, 1602)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 208 155964 002400 263178 911171 511375 753914 674875 342285 138291 375408 > 2²⁰⁷ [i]