MinT - Best Known (55, 55+93, s)-Nets in Base 2

Best Known (55, 55+93, s)-Nets in Base 2

(55, 55+93, 42)-Net over F₂ — Constructive and digital

Digital (55, 148, 42)-net over F₂, using

t-expansion [i] based on digital (54, 148, 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]

(55, 55+93, 107)-Net in Base 2 — Upper bound on s

There is no (55, 148, 108)-net in base 2, because

1 times m-reduction [i] would yield (55, 147, 108)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 233 028209 108570 930560 736956 374907 292492 679392 > 2¹⁴⁷ [i]