MinT - Best Known (210−55, 210, s)-Nets in Base 2

Best Known (210−55, 210, s)-Nets in Base 2

(210−55, 210, 195)-Net over F₂ — Constructive and digital

Digital (155, 210, 195)-net over F₂, using

t-expansion [i] based on digital (154, 210, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 70, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(210−55, 210, 258)-Net over F₂ — Digital

Digital (155, 210, 258)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−55, 210, 2297)-Net in Base 2 — Upper bound on s

There is no (155, 210, 2298)-net in base 2, because

1 times m-reduction [i] would yield (155, 209, 2298)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 832 268481 660008 070641 781153 490817 124570 891071 981020 026599 509164 > 2²⁰⁹ [i]