MinT - Best Known (146−56, 146, s)-Nets in Base 2

Best Known (146−56, 146, s)-Nets in Base 2

(146−56, 146, 66)-Net over F₂ — Constructive and digital

Digital (90, 146, 66)-net over F₂, using

4 times m-reduction [i] based on digital (90, 150, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 75, 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]

(146−56, 146, 80)-Net over F₂ — Digital

Digital (90, 146, 80)-net over F₂, using

trace code for nets [i] based on digital (17, 73, 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]

(146−56, 146, 379)-Net in Base 2 — Upper bound on s

There is no (90, 146, 380)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 90 951499 229353 128425 988113 227845 883454 119512 > 2¹⁴⁶ [i]