MinT - Best Known (113, 113+40, s)-Nets in Base 2

Best Known (113, 113+40, s)-Nets in Base 2

(113, 113+40, 144)-Net over F₂ — Constructive and digital

Digital (113, 153, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 51, 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]

(113, 113+40, 201)-Net over F₂ — Digital

Digital (113, 153, 201)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+40, 1638)-Net in Base 2 — Upper bound on s

There is no (113, 153, 1639)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11459 731171 973147 773776 601201 533497 820988 803814 > 2¹⁵³ [i]