MinT - Best Known (105−63, 105, s)-Nets in Base 2

Best Known (105−63, 105, s)-Nets in Base 2

(105−63, 105, 33)-Net over F₂ — Constructive and digital

Digital (42, 105, 33)-net over F₂, using

t-expansion [i] based on digital (39, 105, 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]

(105−63, 105, 87)-Net in Base 2 — Upper bound on s

There is no (42, 105, 88)-net in base 2, because

1 times m-reduction [i] would yield (42, 104, 88)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 23 438461 352402 925212 202459 814600 > 2¹⁰⁴ [i]