MinT - Best Known (210−72, 210, s)-Nets in Base 2

Best Known (210−72, 210, s)-Nets in Base 2

(210−72, 210, 112)-Net over F₂ — Constructive and digital

Digital (138, 210, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 105, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(210−72, 210, 137)-Net over F₂ — Digital

Digital (138, 210, 137)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−72, 210, 762)-Net in Base 2 — Upper bound on s

There is no (138, 210, 763)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1698 809431 116959 784136 522142 594507 768024 147483 580997 408478 501934 > 2²¹⁰ [i]