MinT - Best Known (71, 71+25, s)-Nets in Base 2

Best Known (71, 71+25, s)-Nets in Base 2

(71, 71+25, 102)-Net over F₂ — Constructive and digital

Digital (71, 96, 102)-net over F₂, using

trace code for nets [i] based on digital (7, 32, 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]

(71, 71+25, 141)-Net over F₂ — Digital

Digital (71, 96, 141)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+25, 1260)-Net in Base 2 — Upper bound on s

There is no (71, 96, 1261)-net in base 2, because

1 times m-reduction [i] would yield (71, 95, 1261)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 39777 287494 598675 669119 211117 > 2⁹⁵ [i]