MinT - Best Known (238−68, 238, s)-Nets in Base 2

Best Known (238−68, 238, s)-Nets in Base 2

(238−68, 238, 144)-Net over F₂ — Constructive and digital

Digital (170, 238, 144)-net over F₂, using

2¹ times duplication [i] based on 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]

(238−68, 238, 233)-Net over F₂ — Digital

Digital (170, 238, 233)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−68, 238, 1682)-Net in Base 2 — Upper bound on s

There is no (170, 238, 1683)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 444213 827584 636440 205243 931843 842733 699400 854773 969149 844573 265082 516148 > 2²³⁸ [i]