MinT - Best Known (105, 105+39, s)-Nets in Base 2

Best Known (105, 105+39, s)-Nets in Base 2

(105, 105+39, 135)-Net over F₂ — Constructive and digital

Digital (105, 144, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 48, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(105, 105+39, 175)-Net over F₂ — Digital

Digital (105, 144, 175)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+39, 1433)-Net in Base 2 — Upper bound on s

There is no (105, 144, 1434)-net in base 2, because

1 times m-reduction [i] would yield (105, 143, 1434)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11 156860 428173 082538 306954 253773 492739 290720 > 2¹⁴³ [i]