MinT - Best Known (105, 105+41, s)-Nets in Base 2

Best Known (105, 105+41, s)-Nets in Base 2

(105, 105+41, 102)-Net over F₂ — Constructive and digital

Digital (105, 146, 102)-net over F₂, using

1 times m-reduction [i] based on digital (105, 147, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 49, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(105, 105+41, 161)-Net over F₂ — Digital

Digital (105, 146, 161)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+41, 1234)-Net in Base 2 — Upper bound on s

There is no (105, 146, 1235)-net in base 2, because

1 times m-reduction [i] would yield (105, 145, 1235)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 44 681265 729710 017149 917830 379490 557997 471128 > 2¹⁴⁵ [i]