MinT - Best Known (101, 101+59, s)-Nets in Base 2

Best Known (101, 101+59, s)-Nets in Base 2

(101, 101+59, 68)-Net over F₂ — Constructive and digital

Digital (101, 160, 68)-net over F₂, using

trace code for nets [i] based on digital (21, 80, 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]

(101, 101+59, 92)-Net over F₂ — Digital

Digital (101, 160, 92)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+59, 480)-Net in Base 2 — Upper bound on s

There is no (101, 160, 481)-net in base 2, because

1 times m-reduction [i] would yield (101, 159, 481)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 753065 044062 352407 046693 521552 678086 834625 833776 > 2¹⁵⁹ [i]