MinT - Best Known (84, 84+63, s)-Nets in Base 2

Best Known (84, 84+63, s)-Nets in Base 2

(84, 84+63, 54)-Net over F₂ — Constructive and digital

Digital (84, 147, 54)-net over F₂, using

1 times m-reduction [i] based on digital (84, 148, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 74, 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]

(84, 84+63, 61)-Net over F₂ — Digital

Digital (84, 147, 61)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+63, 281)-Net in Base 2 — Upper bound on s

There is no (84, 147, 282)-net in base 2, because

1 times m-reduction [i] would yield (84, 146, 282)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 91 909495 309899 228042 579588 014878 692991 083072 > 2¹⁴⁶ [i]