MinT - Best Known (220−49, 220, s)-Nets in Base 2

Best Known (220−49, 220, s)-Nets in Base 2

(220−49, 220, 260)-Net over F₂ — Constructive and digital

Digital (171, 220, 260)-net over F₂, using

trace code for nets [i] based on digital (6, 55, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(220−49, 220, 411)-Net over F₂ — Digital

Digital (171, 220, 411)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−49, 220, 5438)-Net in Base 2 — Upper bound on s

There is no (171, 220, 5439)-net in base 2, because

1 times m-reduction [i] would yield (171, 219, 5439)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 845983 369068 905621 284016 961247 198337 844513 432732 524066 568598 423493 > 2²¹⁹ [i]