MinT - Best Known (39, 39+19, s)-Nets in Base 2

Best Known (39, 39+19, s)-Nets in Base 2

(39, 39+19, 54)-Net over F₂ — Constructive and digital

Digital (39, 58, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 29, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(39, 39+19, 58)-Net over F₂ — Digital

Digital (39, 58, 58)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+19, 321)-Net in Base 2 — Upper bound on s

There is no (39, 58, 322)-net in base 2, because

1 times m-reduction [i] would yield (39, 57, 322)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 145567 605546 551368 > 2⁵⁷ [i]