MinT - Best Known (86, 86+65, s)-Nets in Base 2

Best Known (86, 86+65, s)-Nets in Base 2

(86, 86+65, 54)-Net over F₂ — Constructive and digital

Digital (86, 151, 54)-net over F₂, using

1 times m-reduction [i] based on digital (86, 152, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 76, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(86, 86+65, 62)-Net over F₂ — Digital

Digital (86, 151, 62)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+65, 284)-Net in Base 2 — Upper bound on s

There is no (86, 151, 285)-net in base 2, because

1 times m-reduction [i] would yield (86, 150, 285)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1430 394610 086022 517711 914809 107406 648949 757064 > 2¹⁵⁰ [i]