MinT - Best Known (97, 97+51, s)-Nets in Base 2

Best Known (97, 97+51, s)-Nets in Base 2

(97, 97+51, 68)-Net over F₂ — Constructive and digital

Digital (97, 148, 68)-net over F₂, using

4 times m-reduction [i] based on digital (97, 152, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 76, 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]

(97, 97+51, 101)-Net over F₂ — Digital

Digital (97, 148, 101)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+51, 563)-Net in Base 2 — Upper bound on s

There is no (97, 148, 564)-net in base 2, because

1 times m-reduction [i] would yield (97, 147, 564)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 183 233666 161430 867118 518916 856695 390697 353884 > 2¹⁴⁷ [i]