MinT - Best Known (110, 110+31, s)-Nets in Base 2

Best Known (110, 110+31, s)-Nets in Base 2

(110, 110+31, 195)-Net over F₂ — Constructive and digital

Digital (110, 141, 195)-net over F₂, using

3 times m-reduction [i] based on digital (110, 144, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 48, 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]

(110, 110+31, 298)-Net over F₂ — Digital

Digital (110, 141, 298)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 110+31, 4121)-Net in Base 2 — Upper bound on s

There is no (110, 141, 4122)-net in base 2, because

1 times m-reduction [i] would yield (110, 140, 4122)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 395447 923297 031531 301371 894385 288149 938616 > 2¹⁴⁰ [i]