MinT - Best Known (58−25, 58, s)-Nets in Base 2

Best Known (58−25, 58, s)-Nets in Base 2

(58−25, 58, 30)-Net over F₂ — Constructive and digital

Digital (33, 58, 30)-net over F₂, using

trace code for nets [i] based on digital (4, 29, 15)-net over F₄, using
- net from sequence [i] based on digital (4, 14)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
    - an explicitly constructive algebraic function field [i]

(58−25, 58, 31)-Net over F₂ — Digital

Digital (33, 58, 31)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(58−25, 58, 125)-Net in Base 2 — Upper bound on s

There is no (33, 58, 126)-net in base 2, because

1 times m-reduction [i] would yield (33, 57, 126)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 147493 246130 096571 > 2⁵⁷ [i]