MinT - Best Known (197−75, 197, s)-Nets in Base 2

Best Known (197−75, 197, s)-Nets in Base 2

(197−75, 197, 68)-Net over F₂ — Constructive and digital

Digital (122, 197, 68)-net over F₂, using

5 times m-reduction [i] based on digital (122, 202, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 101, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(197−75, 197, 102)-Net over F₂ — Digital

Digital (122, 197, 102)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−75, 197, 523)-Net in Base 2 — Upper bound on s

There is no (122, 197, 524)-net in base 2, because

1 times m-reduction [i] would yield (122, 196, 524)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 103981 041759 457283 922298 303684 813572 823667 991464 400319 445088 > 2¹⁹⁶ [i]