MinT - Best Known (101, 101+73, s)-Nets in Base 2

Best Known (101, 101+73, s)-Nets in Base 2

(101, 101+73, 60)-Net over F₂ — Constructive and digital

Digital (101, 174, 60)-net over F₂, using

2 times m-reduction [i] based on digital (101, 176, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 88, 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]

(101, 101+73, 74)-Net over F₂ — Digital

Digital (101, 174, 74)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+73, 348)-Net in Base 2 — Upper bound on s

There is no (101, 174, 349)-net in base 2, because

1 times m-reduction [i] would yield (101, 173, 349)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12078 562071 229476 142603 668014 072198 629165 643867 666150 > 2¹⁷³ [i]