MinT - Best Known (80, 80+47, s)-Nets in Base 2

Best Known (80, 80+47, s)-Nets in Base 2

(80, 80+47, 66)-Net over F₂ — Constructive and digital

Digital (80, 127, 66)-net over F₂, using

3 times m-reduction [i] based on digital (80, 130, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 65, 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]

(80, 80+47, 76)-Net over F₂ — Digital

Digital (80, 127, 76)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+47, 387)-Net in Base 2 — Upper bound on s

There is no (80, 127, 388)-net in base 2, because

1 times m-reduction [i] would yield (80, 126, 388)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 87 351142 260356 315430 108506 292887 959072 > 2¹²⁶ [i]