MinT - Best Known (162−46, 162, s)-Nets in Base 2

Best Known (162−46, 162, s)-Nets in Base 2

(162−46, 162, 112)-Net over F₂ — Constructive and digital

Digital (116, 162, 112)-net over F₂, using

4 times m-reduction [i] based on digital (116, 166, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 83, 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]

(162−46, 162, 171)-Net over F₂ — Digital

Digital (116, 162, 171)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−46, 162, 1210)-Net in Base 2 — Upper bound on s

There is no (116, 162, 1211)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 929935 633048 924787 197477 233594 414998 888396 895892 > 2¹⁶² [i]