MinT - Best Known (237−68, 237, s)-Nets in Base 2

Best Known (237−68, 237, s)-Nets in Base 2

(237−68, 237, 144)-Net over F₂ — Constructive and digital

Digital (169, 237, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 79, 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]

(237−68, 237, 230)-Net over F₂ — Digital

Digital (169, 237, 230)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−68, 237, 1647)-Net in Base 2 — Upper bound on s

There is no (169, 237, 1648)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 221909 836247 642134 336515 409727 741022 837320 415482 015266 726252 395132 988803 > 2²³⁷ [i]