MinT - Best Known (220−64, 220, s)-Nets in Base 2

Best Known (220−64, 220, s)-Nets in Base 2

(220−64, 220, 135)-Net over F₂ — Constructive and digital

Digital (156, 220, 135)-net over F₂, using

2¹ times duplication [i] based on digital (155, 219, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 73, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(220−64, 220, 209)-Net over F₂ — Digital

Digital (156, 220, 209)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−64, 220, 1454)-Net in Base 2 — Upper bound on s

There is no (156, 220, 1455)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 704654 553818 392299 999647 694352 552772 666007 528614 021149 822761 197945 > 2²²⁰ [i]