MinT - Best Known (65, 65+25, s)-Nets in Base 2

Best Known (65, 65+25, s)-Nets in Base 2

(65, 65+25, 84)-Net over F₂ — Constructive and digital

Digital (65, 90, 84)-net over F₂, using

trace code for nets [i] based on digital (5, 30, 28)-net over F₈, using
- net from sequence [i] based on digital (5, 27)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
    - a function field by SÃ©mirat [i]

(65, 65+25, 115)-Net over F₂ — Digital

Digital (65, 90, 115)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+25, 886)-Net in Base 2 — Upper bound on s

There is no (65, 90, 887)-net in base 2, because

1 times m-reduction [i] would yield (65, 89, 887)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 624 735233 918295 850852 090794 > 2⁸⁹ [i]