MinT - Best Known (239−44, 239, s)-Nets in Base 2

Best Known (239−44, 239, s)-Nets in Base 2

(239−44, 239, 320)-Net over F₂ — Constructive and digital

Digital (195, 239, 320)-net over F₂, using

1 times m-reduction [i] based on digital (195, 240, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 48, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(239−44, 239, 785)-Net over F₂ — Digital

Digital (195, 239, 785)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−44, 239, 16838)-Net in Base 2 — Upper bound on s

There is no (195, 239, 16839)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 884297 832995 818810 913278 608745 038657 336052 014370 456428 053875 020699 863396 > 2²³⁹ [i]