MinT - Best Known (127, 127+83, s)-Nets in Base 2

Best Known (127, 127+83, s)-Nets in Base 2

(127, 127+83, 68)-Net over F₂ — Constructive and digital

Digital (127, 210, 68)-net over F₂, using

2 times m-reduction [i] based on digital (127, 212, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 106, 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]

(127, 127+83, 99)-Net over F₂ — Digital

Digital (127, 210, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+83, 494)-Net in Base 2 — Upper bound on s

There is no (127, 210, 495)-net in base 2, because

1 times m-reduction [i] would yield (127, 209, 495)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 851 940706 122611 637097 655030 930961 113017 737248 754031 359999 483208 > 2²⁰⁹ [i]