MinT - Best Known (254−71, 254, s)-Nets in Base 2

Best Known (254−71, 254, s)-Nets in Base 2

(254−71, 254, 144)-Net over F₂ — Constructive and digital

Digital (183, 254, 144)-net over F₂, using

4 times m-reduction [i] based on digital (183, 258, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 86, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(254−71, 254, 259)-Net over F₂ — Digital

Digital (183, 254, 259)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−71, 254, 2034)-Net in Base 2 — Upper bound on s

There is no (183, 254, 2035)-net in base 2, because

1 times m-reduction [i] would yield (183, 253, 2035)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14614 515582 094494 072127 332597 424803 292337 122227 637022 592551 311221 427941 470654 > 2²⁵³ [i]