MinT - Best Known (66, 66+42, s)-Nets in Base 2

Best Known (66, 66+42, s)-Nets in Base 2

(66, 66+42, 56)-Net over F₂ — Constructive and digital

Digital (66, 108, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 54, 28)-net over F₄, using
- net from sequence [i] based on digital (12, 27)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(66, 66+42, 60)-Net over F₂ — Digital

Digital (66, 108, 60)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+42, 277)-Net in Base 2 — Upper bound on s

There is no (66, 108, 278)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 347 467440 995566 609322 717574 821539 > 2¹⁰⁸ [i]