MinT - Best Known (122, 122+77, s)-Nets in Base 2

Best Known (122, 122+77, s)-Nets in Base 2

(122, 122+77, 68)-Net over F₂ — Constructive and digital

Digital (122, 199, 68)-net over F₂, using

3 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]

(122, 122+77, 99)-Net over F₂ — Digital

Digital (122, 199, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(122, 122+77, 502)-Net in Base 2 — Upper bound on s

There is no (122, 199, 503)-net in base 2, because

1 times m-reduction [i] would yield (122, 198, 503)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 421162 830629 794577 292439 529930 860453 654058 148122 411800 415589 > 2¹⁹⁸ [i]