MinT - Best Known (58, 165, s)-Nets in Base 2

Best Known (58, 165, s)-Nets in Base 2

(58, 165, 42)-Net over F₂ — Constructive and digital

Digital (58, 165, 42)-net over F₂, using

t-expansion [i] based on digital (54, 165, 42)-net over F₂, using
- net from sequence [i] based on digital (54, 41)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(58, 165, 110)-Net in Base 2 — Upper bound on s

There is no (58, 165, 111)-net in base 2, because

1 times m-reduction [i] would yield (58, 164, 111)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 31 544875 363194 809686 516993 393385 309955 196974 611568 > 2¹⁶⁴ [i]