MinT - Best Known (237−82, 237, s)-Nets in Base 2

Best Known (237−82, 237, s)-Nets in Base 2

(237−82, 237, 112)-Net over F₂ — Constructive and digital

Digital (155, 237, 112)-net over F₂, using

7 times m-reduction [i] based on digital (155, 244, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 122, 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]

(237−82, 237, 148)-Net over F₂ — Digital

Digital (155, 237, 148)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−82, 237, 828)-Net in Base 2 — Upper bound on s

There is no (155, 237, 829)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 230950 722692 109330 128007 427911 833804 065714 189932 238132 037344 724803 898650 > 2²³⁷ [i]