MinT - Best Known (84, 84+37, s)-Nets in Base 2

Best Known (84, 84+37, s)-Nets in Base 2

(84, 84+37, 72)-Net over F₂ — Constructive and digital

Digital (84, 121, 72)-net over F₂, using

2¹ times duplication [i] based on digital (83, 120, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 40, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]

(84, 84+37, 113)-Net over F₂ — Digital

Digital (84, 121, 113)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+37, 741)-Net in Base 2 — Upper bound on s

There is no (84, 121, 742)-net in base 2, because

1 times m-reduction [i] would yield (84, 120, 742)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 352379 516209 595218 946697 408194 494420 > 2¹²⁰ [i]