MinT - Best Known (124, 204, s)-Nets in Base 2

Best Known (124, 204, s)-Nets in Base 2

(124, 204, 68)-Net over F₂ — Constructive and digital

Digital (124, 204, 68)-net over F₂, using

2 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, 204, 98)-Net over F₂ — Digital

Digital (124, 204, 98)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 204, 484)-Net in Base 2 — Upper bound on s

There is no (124, 204, 485)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27 418018 960460 007572 033048 421866 883423 946044 853966 514408 145480 > 2²⁰⁴ [i]