MinT - Best Known (240−86, 240, s)-Nets in Base 2

Best Known (240−86, 240, s)-Nets in Base 2

(240−86, 240, 112)-Net over F₂ — Constructive and digital

Digital (154, 240, 112)-net over F₂, using

2 times m-reduction [i] based on digital (154, 242, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 121, 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]

(240−86, 240, 138)-Net over F₂ — Digital

Digital (154, 240, 138)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−86, 240, 746)-Net in Base 2 — Upper bound on s

There is no (154, 240, 747)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 800867 515110 988333 505959 494433 173171 899524 127846 756726 360265 187330 070690 > 2²⁴⁰ [i]