MinT - Best Known (71, 71+22, s)-Nets in Base 2

Best Known (71, 71+22, s)-Nets in Base 2

(71, 71+22, 135)-Net over F₂ — Constructive and digital

Digital (71, 93, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 31, 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]

(71, 71+22, 179)-Net over F₂ — Digital

Digital (71, 93, 179)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+22, 1706)-Net in Base 2 — Upper bound on s

There is no (71, 93, 1707)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 9949 429613 189174 461362 147614 > 2⁹³ [i]