MinT - Best Known (150, 150+63, s)-Nets in Base 2

Best Known (150, 150+63, s)-Nets in Base 2

(150, 150+63, 112)-Net over F₂ — Constructive and digital

Digital (150, 213, 112)-net over F₂, using

21 times m-reduction [i] based on digital (150, 234, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 117, 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]

(150, 150+63, 195)-Net over F₂ — Digital

Digital (150, 213, 195)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+63, 1375)-Net in Base 2 — Upper bound on s

There is no (150, 213, 1376)-net in base 2, because

1 times m-reduction [i] would yield (150, 212, 1376)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6584 537770 450746 072781 101543 173398 949893 585263 223416 453596 770443 > 2²¹² [i]