MinT - Best Known (216−48, 216, s)-Nets in Base 2

Best Known (216−48, 216, s)-Nets in Base 2

(216−48, 216, 260)-Net over F₂ — Constructive and digital

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]

(216−48, 216, 408)-Net over F₂ — Digital

Digital (168, 216, 408)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−48, 216, 4983)-Net in Base 2 — Upper bound on s

There is no (168, 216, 4984)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 105416 369040 981132 839371 876181 121046 137749 722028 003201 366562 296876 > 2²¹⁶ [i]