MinT - Best Known (106−39, 106, s)-Nets in Base 2

Best Known (106−39, 106, s)-Nets in Base 2

(106−39, 106, 60)-Net over F₂ — Constructive and digital

Digital (67, 106, 60)-net over F₂, using

2 times m-reduction [i] based on digital (67, 108, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 54, 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]

(106−39, 106, 67)-Net over F₂ — Digital

Digital (67, 106, 67)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−39, 106, 338)-Net in Base 2 — Upper bound on s

There is no (67, 106, 339)-net in base 2, because

1 times m-reduction [i] would yield (67, 105, 339)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 41 929140 143196 623771 491590 927086 > 2¹⁰⁵ [i]