MinT - Best Known (240−105, 240, s)-Nets in Base 2

Best Known (240−105, 240, s)-Nets in Base 2

(240−105, 240, 66)-Net over F₂ — Constructive and digital

Digital (135, 240, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 120, 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]

(240−105, 240, 88)-Net over F₂ — Digital

Digital (135, 240, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−105, 240, 416)-Net in Base 2 — Upper bound on s

There is no (135, 240, 417)-net in base 2, because

1 times m-reduction [i] would yield (135, 239, 417)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 896496 704510 519921 990979 728587 131160 876858 553876 096269 672777 694808 731104 > 2²³⁹ [i]