MinT - Best Known (151−54, 151, s)-Nets in Base 2

Best Known (151−54, 151, s)-Nets in Base 2

(151−54, 151, 68)-Net over F₂ — Constructive and digital

Digital (97, 151, 68)-net over F₂, using

1 times m-reduction [i] based on digital (97, 152, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 76, 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]

(151−54, 151, 95)-Net over F₂ — Digital

Digital (97, 151, 95)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−54, 151, 488)-Net in Base 2 — Upper bound on s

There is no (97, 151, 489)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2929 676110 424465 093313 045812 248868 629784 450864 > 2¹⁵¹ [i]