MinT - Best Known (180−39, 180, s)-Nets in Base 2

Best Known (180−39, 180, s)-Nets in Base 2

(180−39, 180, 260)-Net over F₂ — Constructive and digital

Digital (141, 180, 260)-net over F₂, using

trace code for nets [i] based on digital (6, 45, 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]

(180−39, 180, 376)-Net over F₂ — Digital

Digital (141, 180, 376)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−39, 180, 5407)-Net in Base 2 — Upper bound on s

There is no (141, 180, 5408)-net in base 2, because

1 times m-reduction [i] would yield (141, 179, 5408)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 767565 592237 062495 923713 581219 581511 627533 635486 106115 > 2¹⁷⁹ [i]