MinT - Best Known (150−56, 150, s)-Nets in Base 2

Best Known (150−56, 150, s)-Nets in Base 2

(150−56, 150, 66)-Net over F₂ — Constructive and digital

Digital (94, 150, 66)-net over F₂, using

8 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]

(150−56, 150, 85)-Net over F₂ — Digital

Digital (94, 150, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−56, 150, 423)-Net in Base 2 — Upper bound on s

There is no (94, 150, 424)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1497 336318 857431 626806 924767 155140 814776 444764 > 2¹⁵⁰ [i]