MinT - Best Known (199−79, 199, s)-Nets in Base 2

Best Known (199−79, 199, s)-Nets in Base 2

(199−79, 199, 66)-Net over F₂ — Constructive and digital

Digital (120, 199, 66)-net over F₂, using

11 times m-reduction [i] based on digital (120, 210, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 105, 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]

(199−79, 199, 93)-Net over F₂ — Digital

Digital (120, 199, 93)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−79, 199, 464)-Net in Base 2 — Upper bound on s

There is no (120, 199, 465)-net in base 2, because

1 times m-reduction [i] would yield (120, 198, 465)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 418252 473943 937710 069599 481132 451551 458817 680369 857442 600960 > 2¹⁹⁸ [i]