MinT - Best Known (80, 80+37, s)-Nets in Base 2

Best Known (80, 80+37, s)-Nets in Base 2

(80, 80+37, 68)-Net over F₂ — Constructive and digital

Digital (80, 117, 68)-net over F₂, using

1 times m-reduction [i] based on digital (80, 118, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 59, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(80, 80+37, 102)-Net over F₂ — Digital

Digital (80, 117, 102)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+37, 631)-Net in Base 2 — Upper bound on s

There is no (80, 117, 632)-net in base 2, because

1 times m-reduction [i] would yield (80, 116, 632)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 83565 483962 307276 796366 802683 941755 > 2¹¹⁶ [i]