MinT - Best Known (54, 54+71, s)-Nets in Base 2

Best Known (54, 54+71, s)-Nets in Base 2

(54, 54+71, 42)-Net over F₂ — Constructive and digital

Digital (54, 125, 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]

(54, 54+71, 116)-Net in Base 2 — Upper bound on s

There is no (54, 125, 117)-net in base 2, because

1 times m-reduction [i] would yield (54, 124, 117)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 23 210463 916231 194494 298529 444135 118304 > 2¹²⁴ [i]