MinT - Best Known (66−29, 66, s)-Nets in Base 2

Best Known (66−29, 66, s)-Nets in Base 2

(66−29, 66, 30)-Net over F₂ — Constructive and digital

Digital (37, 66, 30)-net over F₂, using

trace code for nets [i] based on digital (4, 33, 15)-net over F₄, using
- net from sequence [i] based on digital (4, 14)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
    - an explicitly constructive algebraic function field [i]

(66−29, 66, 32)-Net over F₂ — Digital

Digital (37, 66, 32)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(66−29, 66, 131)-Net in Base 2 — Upper bound on s

There is no (37, 66, 132)-net in base 2, because

1 times m-reduction [i] would yield (37, 65, 132)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 37 886675 008173 125664 > 2⁶⁵ [i]