MinT - Best Known (197, 197+45, s)-Nets in Base 2

Best Known (197, 197+45, s)-Nets in Base 2

(197, 197+45, 320)-Net over F₂ — Constructive and digital

Digital (197, 242, 320)-net over F₂, using

2² times duplication [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+45, 767)-Net over F₂ — Digital

Digital (197, 242, 767)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197, 197+45, 17935)-Net in Base 2 — Upper bound on s

There is no (197, 242, 17936)-net in base 2, because

1 times m-reduction [i] would yield (197, 241, 17936)-net in base 2, but
- 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]