MinT - Best Known (105−41, 105, s)-Nets in Base 2

Best Known (105−41, 105, s)-Nets in Base 2

(105−41, 105, 54)-Net over F₂ — Constructive and digital

Digital (64, 105, 54)-net over F₂, using

3 times m-reduction [i] based on digital (64, 108, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 54, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(105−41, 105, 58)-Net over F₂ — Digital

Digital (64, 105, 58)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−41, 105, 276)-Net in Base 2 — Upper bound on s

There is no (64, 105, 277)-net in base 2, because

1 times m-reduction [i] would yield (64, 104, 277)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20 300145 589615 323075 737212 515121 > 2¹⁰⁴ [i]