MinT - Best Known (84−23, 84, s)-Nets in Base 2

Best Known (84−23, 84, s)-Nets in Base 2

(84−23, 84, 84)-Net over F₂ — Constructive and digital

Digital (61, 84, 84)-net over F₂, using

trace code for nets [i] based on digital (5, 28, 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]

(84−23, 84, 113)-Net over F₂ — Digital

Digital (61, 84, 113)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−23, 84, 901)-Net in Base 2 — Upper bound on s

There is no (61, 84, 902)-net in base 2, because

1 times m-reduction [i] would yield (61, 83, 902)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 9 760403 095385 784789 550752 > 2⁸³ [i]