MinT - Best Known (109, 109+74, s)-Nets in Base 2

Best Known (109, 109+74, s)-Nets in Base 2

(109, 109+74, 66)-Net over F₂ — Constructive and digital

Digital (109, 183, 66)-net over F₂, using

5 times m-reduction [i] based on digital (109, 188, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 94, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(109, 109+74, 84)-Net over F₂ — Digital

Digital (109, 183, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+74, 399)-Net in Base 2 — Upper bound on s

There is no (109, 183, 400)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12 765889 917686 878699 555892 967367 092006 588716 438409 343412 > 2¹⁸³ [i]