MinT - Best Known (223−90, 223, s)-Nets in Base 2

Best Known (223−90, 223, s)-Nets in Base 2

(223−90, 223, 68)-Net over F₂ — Constructive and digital

Digital (133, 223, 68)-net over F₂, using

1 times m-reduction [i] based on digital (133, 224, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 112, 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]

(223−90, 223, 99)-Net over F₂ — Digital

Digital (133, 223, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−90, 223, 483)-Net in Base 2 — Upper bound on s

There is no (133, 223, 484)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14 087749 840772 166666 787374 120672 277186 056806 830838 208983 256555 229168 > 2²²³ [i]