MinT - Best Known (198−81, 198, s)-Nets in Base 2

Best Known (198−81, 198, s)-Nets in Base 2

(198−81, 198, 66)-Net over F₂ — Constructive and digital

Digital (117, 198, 66)-net over F₂, using

6 times m-reduction [i] based on digital (117, 204, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 102, 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]

(198−81, 198, 87)-Net over F₂ — Digital

Digital (117, 198, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−81, 198, 422)-Net in Base 2 — Upper bound on s

There is no (117, 198, 423)-net in base 2, because

1 times m-reduction [i] would yield (117, 197, 423)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 206042 411362 835483 648611 543285 862088 239708 991463 781814 103488 > 2¹⁹⁷ [i]