MinT - Best Known (134−45, 134, s)-Nets in Base 2

Best Known (134−45, 134, s)-Nets in Base 2

(134−45, 134, 68)-Net over F₂ — Constructive and digital

Digital (89, 134, 68)-net over F₂, using

2 times m-reduction [i] based on digital (89, 136, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 68, 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]

(134−45, 134, 99)-Net over F₂ — Digital

Digital (89, 134, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−45, 134, 566)-Net in Base 2 — Upper bound on s

There is no (89, 134, 567)-net in base 2, because

1 times m-reduction [i] would yield (89, 133, 567)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11172 333092 288744 368177 128538 356883 428811 > 2¹³³ [i]