MinT - Best Known (213−45, 213, s)-Nets in Base 2

Best Known (213−45, 213, s)-Nets in Base 2

(213−45, 213, 260)-Net over F₂ — Constructive and digital

Digital (168, 213, 260)-net over F₂, using

3 times m-reduction [i] based on digital (168, 216, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 54, 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]

(213−45, 213, 464)-Net over F₂ — Digital

Digital (168, 213, 464)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−45, 213, 7173)-Net in Base 2 — Upper bound on s

There is no (168, 213, 7174)-net in base 2, because

1 times m-reduction [i] would yield (168, 212, 7174)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6592 976741 655845 208846 646530 385641 918677 536442 385894 131909 054464 > 2²¹² [i]