MinT - Best Known (216−44, 216, s)-Nets in Base 2

Best Known (216−44, 216, s)-Nets in Base 2

(216−44, 216, 260)-Net over F₂ — Constructive and digital

Digital (172, 216, 260)-net over F₂, using

t-expansion [i] based on digital (171, 216, 260)-net over F₂, using
- 4 times m-reduction [i] based on 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]

(216−44, 216, 523)-Net over F₂ — Digital

Digital (172, 216, 523)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−44, 216, 8141)-Net in Base 2 — Upper bound on s

There is no (172, 216, 8142)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 105514 219743 574369 576849 681495 011717 992016 319796 204566 407247 959216 > 2²¹⁶ [i]