MinT - Best Known (79, 79+42, s)-Nets in Base 2

Best Known (79, 79+42, s)-Nets in Base 2

(79, 79+42, 66)-Net over F₂ — Constructive and digital

Digital (79, 121, 66)-net over F₂, using

7 times m-reduction [i] based on digital (79, 128, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 64, 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]

(79, 79+42, 85)-Net over F₂ — Digital

Digital (79, 121, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+42, 440)-Net in Base 2 — Upper bound on s

There is no (79, 121, 441)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 673600 445524 965051 252487 752247 076084 > 2¹²¹ [i]