MinT - Best Known (148−57, 148, s)-Nets in Base 2

Best Known (148−57, 148, s)-Nets in Base 2

(148−57, 148, 66)-Net over F₂ — Constructive and digital

Digital (91, 148, 66)-net over F₂, using

4 times m-reduction [i] based on digital (91, 152, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 76, 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]

(148−57, 148, 80)-Net over F₂ — Digital

Digital (91, 148, 80)-net over F₂, using

trace code for nets [i] based on digital (17, 74, 40)-net over F₄, using
- net from sequence [i] based on digital (17, 39)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 17 and N(F) ≥ 40, using
    - Drinfeld modules of rank 1 [i]

(148−57, 148, 390)-Net in Base 2 — Upper bound on s

There is no (91, 148, 391)-net in base 2, because

1 times m-reduction [i] would yield (91, 147, 391)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 188 199695 172234 489953 409585 039927 356903 192816 > 2¹⁴⁷ [i]