MinT - Best Known (237−70, 237, s)-Nets in Base 2

Best Known (237−70, 237, s)-Nets in Base 2

(237−70, 237, 135)-Net over F₂ — Constructive and digital

Digital (167, 237, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 79, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(237−70, 237, 214)-Net over F₂ — Digital

Digital (167, 237, 214)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−70, 237, 1468)-Net in Base 2 — Upper bound on s

There is no (167, 237, 1469)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 225057 595241 120369 963762 311988 133200 354661 689185 141951 238379 258177 598720 > 2²³⁷ [i]