MinT - Best Known (135−38, 135, s)-Nets in Base 2

Best Known (135−38, 135, s)-Nets in Base 2

(135−38, 135, 102)-Net over F₂ — Constructive and digital

Digital (97, 135, 102)-net over F₂, using

trace code for nets [i] based on digital (7, 45, 34)-net over F₈, using
- net from sequence [i] based on digital (7, 33)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(135−38, 135, 151)-Net over F₂ — Digital

Digital (97, 135, 151)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−38, 135, 1064)-Net in Base 2 — Upper bound on s

There is no (97, 135, 1065)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 44285 077054 213493 338642 801943 067031 416848 > 2¹³⁵ [i]