MinT - Best Known (157, 157+83, s)-Nets in Base 2

Best Known (157, 157+83, s)-Nets in Base 2

(157, 157+83, 112)-Net over F₂ — Constructive and digital

Digital (157, 240, 112)-net over F₂, using

8 times m-reduction [i] based on digital (157, 248, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 124, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(157, 157+83, 150)-Net over F₂ — Digital

Digital (157, 240, 150)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 157+83, 858)-Net in Base 2 — Upper bound on s

There is no (157, 240, 859)-net in base 2, because

1 times m-reduction [i] would yield (157, 239, 859)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 904002 416394 726812 523635 310350 435550 838440 413445 063815 764619 979654 859320 > 2²³⁹ [i]