MinT - Best Known (89−28, 89, s)-Nets in Base 2

Best Known (89−28, 89, s)-Nets in Base 2

(89−28, 89, 66)-Net over F₂ — Constructive and digital

Digital (61, 89, 66)-net over F₂, using

3 times m-reduction [i] based on digital (61, 92, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 46, 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]

(89−28, 89, 84)-Net over F₂ — Digital

Digital (61, 89, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−28, 89, 475)-Net in Base 2 — Upper bound on s

There is no (61, 89, 476)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 627 872202 317696 557478 979804 > 2⁸⁹ [i]