MinT - Best Known (235−83, 235, s)-Nets in Base 2

Best Known (235−83, 235, s)-Nets in Base 2

(235−83, 235, 112)-Net over F₂ — Constructive and digital

Digital (152, 235, 112)-net over F₂, using

3 times m-reduction [i] based on digital (152, 238, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 119, 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]

(235−83, 235, 140)-Net over F₂ — Digital

Digital (152, 235, 140)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−83, 235, 784)-Net in Base 2 — Upper bound on s

There is no (152, 235, 785)-net in base 2, because

1 times m-reduction [i] would yield (152, 234, 785)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28630 514605 514813 773109 962098 829893 008631 389201 227692 489679 861203 740000 > 2²³⁴ [i]