MinT - Best Known (124, 124+77, s)-Nets in Base 2

Best Known (124, 124+77, s)-Nets in Base 2

(124, 124+77, 68)-Net over F₂ — Constructive and digital

Digital (124, 201, 68)-net over F₂, using

5 times m-reduction [i] based on digital (124, 206, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 103, 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]

(124, 124+77, 102)-Net over F₂ — Digital

Digital (124, 201, 102)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+77, 522)-Net in Base 2 — Upper bound on s

There is no (124, 201, 523)-net in base 2, because

1 times m-reduction [i] would yield (124, 200, 523)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 617928 859246 864986 550025 721646 696494 959226 704362 151427 380576 > 2²⁰⁰ [i]