MinT - Best Known (222−94, 222, s)-Nets in Base 2

Best Known (222−94, 222, s)-Nets in Base 2

(222−94, 222, 66)-Net over F₂ — Constructive and digital

Digital (128, 222, 66)-net over F₂, using

4 times m-reduction [i] based on digital (128, 226, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 113, 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]

(222−94, 222, 89)-Net over F₂ — Digital

Digital (128, 222, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−94, 222, 419)-Net in Base 2 — Upper bound on s

There is no (128, 222, 420)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 038191 900009 924616 147389 400691 985597 616102 494247 391303 261731 591136 > 2²²² [i]