MinT - Best Known (155, 214, s)-Nets in Base 2

Best Known (155, 214, s)-Nets in Base 2

(155, 214, 144)-Net over F₂ — Constructive and digital

Digital (155, 214, 144)-net over F₂, using

2 times m-reduction [i] based on digital (155, 216, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 72, 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]

(155, 214, 231)-Net over F₂ — Digital

Digital (155, 214, 231)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(155, 214, 1854)-Net in Base 2 — Upper bound on s

There is no (155, 214, 1855)-net in base 2, because

1 times m-reduction [i] would yield (155, 213, 1855)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13216 865045 202550 338621 296184 955097 859812 580476 742710 828773 912276 > 2²¹³ [i]