MinT - Best Known (63−41, 63, s)-Nets in Base 2

Best Known (63−41, 63, s)-Nets in Base 2

(63−41, 63, 21)-Net over F₂ — Constructive and digital

Digital (22, 63, 21)-net over F₂, using

t-expansion [i] based on digital (21, 63, 21)-net over F₂, using
- net from sequence [i] based on digital (21, 20)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(63−41, 63, 46)-Net in Base 2 — Upper bound on s

There is no (22, 63, 47)-net in base 2, because

1 times m-reduction [i] would yield (22, 62, 47)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 681400 633246 447386 > 2⁶² [i]