MinT - Best Known (148−55, 148, s)-Nets in Base 2

Best Known (148−55, 148, s)-Nets in Base 2

(148−55, 148, 66)-Net over F₂ — Constructive and digital

Digital (93, 148, 66)-net over F₂, using

8 times m-reduction [i] based on digital (93, 156, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 78, 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]

(148−55, 148, 85)-Net over F₂ — Digital

Digital (93, 148, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−55, 148, 437)-Net in Base 2 — Upper bound on s

There is no (93, 148, 438)-net in base 2, because

1 times m-reduction [i] would yield (93, 147, 438)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 186 881795 019131 018762 838710 007167 156944 465272 > 2¹⁴⁷ [i]