MinT - Best Known (222−95, 222, s)-Nets in Base 2

Best Known (222−95, 222, s)-Nets in Base 2

(222−95, 222, 66)-Net over F₂ — Constructive and digital

Digital (127, 222, 66)-net over F₂, using

2 times m-reduction [i] based on digital (127, 224, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 112, 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]

(222−95, 222, 86)-Net over F₂ — Digital

Digital (127, 222, 86)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−95, 222, 412)-Net in Base 2 — Upper bound on s

There is no (127, 222, 413)-net in base 2, because

1 times m-reduction [i] would yield (127, 221, 413)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 537229 929488 729892 744007 984013 556232 083102 197646 415959 382334 892256 > 2²²¹ [i]