MinT - Best Known (230−100, 230, s)-Nets in Base 2

Best Known (230−100, 230, s)-Nets in Base 2

(230−100, 230, 66)-Net over F₂ — Constructive and digital

Digital (130, 230, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 115, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(230−100, 230, 86)-Net over F₂ — Digital

Digital (130, 230, 86)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−100, 230, 402)-Net in Base 2 — Upper bound on s

There is no (130, 230, 403)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1734 994748 689103 027662 946171 895644 702845 405360 618205 538760 842700 578268 > 2²³⁰ [i]