MinT - Best Known (114, 114+73, s)-Nets in Base 2

Best Known (114, 114+73, s)-Nets in Base 2

(114, 114+73, 66)-Net over F₂ — Constructive and digital

Digital (114, 187, 66)-net over F₂, using

11 times m-reduction [i] based on digital (114, 198, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 99, 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]

(114, 114+73, 92)-Net over F₂ — Digital

Digital (114, 187, 92)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+73, 461)-Net in Base 2 — Upper bound on s

There is no (114, 187, 462)-net in base 2, because

1 times m-reduction [i] would yield (114, 186, 462)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 99 157484 127710 170189 472468 312607 152147 918086 566908 048630 > 2¹⁸⁶ [i]