MinT - Best Known (252−54, 252, s)-Nets in Base 2

Best Known (252−54, 252, s)-Nets in Base 2

(252−54, 252, 260)-Net over F₂ — Constructive and digital

Digital (198, 252, 260)-net over F₂, using

4 times m-reduction [i] based on digital (198, 256, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 64, 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]

(252−54, 252, 514)-Net over F₂ — Digital

Digital (198, 252, 514)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−54, 252, 7007)-Net in Base 2 — Upper bound on s

There is no (198, 252, 7008)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7254 777434 053440 938615 020523 639337 340360 466803 776428 667100 253449 708363 178451 > 2²⁵² [i]