MinT - Best Known (109, 109+66, s)-Nets in Base 2

Best Known (109, 109+66, s)-Nets in Base 2

(109, 109+66, 68)-Net over F₂ — Constructive and digital

Digital (109, 175, 68)-net over F₂, using

1 times m-reduction [i] based on digital (109, 176, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 88, 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]

(109, 109+66, 94)-Net over F₂ — Digital

Digital (109, 175, 94)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+66, 472)-Net in Base 2 — Upper bound on s

There is no (109, 175, 473)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 48890 385944 955451 346409 876005 466967 942369 814174 786780 > 2¹⁷⁵ [i]