MinT - Best Known (126−28, 126, s)-Nets in Base 2

Best Known (126−28, 126, s)-Nets in Base 2

(126−28, 126, 195)-Net over F₂ — Constructive and digital

Digital (98, 126, 195)-net over F₂, using

trace code for nets [i] based on digital (14, 42, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(126−28, 126, 265)-Net over F₂ — Digital

Digital (98, 126, 265)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−28, 126, 3075)-Net in Base 2 — Upper bound on s

There is no (98, 126, 3076)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 85 441075 813466 170345 666358 204722 119424 > 2¹²⁶ [i]