MinT - Best Known (117−77, 117, s)-Nets in Base 2

Best Known (117−77, 117, s)-Nets in Base 2

(117−77, 117, 33)-Net over F₂ — Constructive and digital

Digital (40, 117, 33)-net over F₂, using

t-expansion [i] based on digital (39, 117, 33)-net over F₂, using
- net from sequence [i] based on digital (39, 32)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(117−77, 117, 77)-Net in Base 2 — Upper bound on s

There is no (40, 117, 78)-net in base 2, because

1 times m-reduction [i] would yield (40, 116, 78)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 93233 047144 613184 700589 635546 630120 > 2¹¹⁶ [i]