MinT - Best Known (235−82, 235, s)-Nets in Base 2

Best Known (235−82, 235, s)-Nets in Base 2

(235−82, 235, 112)-Net over F₂ — Constructive and digital

Digital (153, 235, 112)-net over F₂, using

5 times m-reduction [i] based on digital (153, 240, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 120, 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]

(235−82, 235, 144)-Net over F₂ — Digital

Digital (153, 235, 144)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−82, 235, 798)-Net in Base 2 — Upper bound on s

There is no (153, 235, 799)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 56283 451032 712274 119804 491048 089387 325755 438666 656572 739941 936284 374080 > 2²³⁵ [i]