MinT - Best Known (240−80, 240, s)-Nets in Base 2

Best Known (240−80, 240, s)-Nets in Base 2

(240−80, 240, 112)-Net over F₂ — Constructive and digital

Digital (160, 240, 112)-net over F₂, using

14 times m-reduction [i] based on digital (160, 254, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 127, 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]

(240−80, 240, 163)-Net over F₂ — Digital

Digital (160, 240, 163)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−80, 240, 951)-Net in Base 2 — Upper bound on s

There is no (160, 240, 952)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 820751 319893 688659 177587 990508 882168 657407 199042 958640 056274 796134 605990 > 2²⁴⁰ [i]