MinT - Best Known (196, 196+44, s)-Nets in Base 2

Best Known (196, 196+44, s)-Nets in Base 2

(196, 196+44, 320)-Net over F₂ — Constructive and digital

Digital (196, 240, 320)-net over F₂, using

t-expansion [i] based on digital (195, 240, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 48, 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]

(196, 196+44, 799)-Net over F₂ — Digital

Digital (196, 240, 799)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(196, 196+44, 17378)-Net in Base 2 — Upper bound on s

There is no (196, 240, 17379)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 768537 803016 686151 169852 932559 343390 473674 482837 406179 341072 216291 238824 > 2²⁴⁰ [i]