MinT - Best Known (148−54, 148, s)-Nets in Base 2

Best Known (148−54, 148, s)-Nets in Base 2

(148−54, 148, 66)-Net over F₂ — Constructive and digital

Digital (94, 148, 66)-net over F₂, using

10 times m-reduction [i] based on digital (94, 158, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 79, 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]

(148−54, 148, 89)-Net over F₂ — Digital

Digital (94, 148, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−54, 148, 449)-Net in Base 2 — Upper bound on s

There is no (94, 148, 450)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 366 453772 967272 147115 516881 907635 780339 810944 > 2¹⁴⁸ [i]