MinT - Best Known (230−64, 230, s)-Nets in Base 2

Best Known (230−64, 230, s)-Nets in Base 2

(230−64, 230, 144)-Net over F₂ — Constructive and digital

Digital (166, 230, 144)-net over F₂, using

t-expansion [i] based on digital (165, 230, 144)-net over F₂, using
- 1 times m-reduction [i] based on digital (165, 231, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 77, 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]

(230−64, 230, 241)-Net over F₂ — Digital

Digital (166, 230, 241)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−64, 230, 1817)-Net in Base 2 — Upper bound on s

There is no (166, 230, 1818)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1742 629330 331470 306620 734167 006172 087757 001042 203807 110253 865536 871800 > 2²³⁰ [i]