MinT - Best Known (150−53, 150, s)-Nets in Base 2

Best Known (150−53, 150, s)-Nets in Base 2

(150−53, 150, 68)-Net over F₂ — Constructive and digital

Digital (97, 150, 68)-net over F₂, using

2 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]

(150−53, 150, 97)-Net over F₂ — Digital

Digital (97, 150, 97)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−53, 150, 522)-Net in Base 2 — Upper bound on s

There is no (97, 150, 523)-net in base 2, because

1 times m-reduction [i] would yield (97, 149, 523)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 714 577335 503332 818480 853836 415277 393260 192928 > 2¹⁴⁹ [i]