MinT - Best Known (197, 197+44, s)-Nets in Base 2

Best Known (197, 197+44, s)-Nets in Base 2

(197, 197+44, 320)-Net over F₂ — Constructive and digital

Digital (197, 241, 320)-net over F₂, using

2¹ times duplication [i] based on 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]

(197, 197+44, 813)-Net over F₂ — Digital

Digital (197, 241, 813)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197, 197+44, 17935)-Net in Base 2 — Upper bound on s

There is no (197, 241, 17936)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 535731 540903 992623 999043 009361 956454 319884 667276 302786 119572 461586 496736 > 2²⁴¹ [i]