MinT - Best Known (106, 106+77, s)-Nets in Base 2

Best Known (106, 106+77, s)-Nets in Base 2

(106, 106+77, 60)-Net over F₂ — Constructive and digital

Digital (106, 183, 60)-net over F₂, using

3 times m-reduction [i] based on digital (106, 186, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 93, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(106, 106+77, 76)-Net over F₂ — Digital

Digital (106, 183, 76)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+77, 362)-Net in Base 2 — Upper bound on s

There is no (106, 183, 363)-net in base 2, because

1 times m-reduction [i] would yield (106, 182, 363)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 551587 690573 354463 699608 631670 043061 830062 761732 456814 > 2¹⁸² [i]