MinT - Best Known (200−48, 200, s)-Nets in Base 2

Best Known (200−48, 200, s)-Nets in Base 2

(200−48, 200, 195)-Net over F₂ — Constructive and digital

Digital (152, 200, 195)-net over F₂, using

7 times m-reduction [i] based on digital (152, 207, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 69, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(200−48, 200, 312)-Net over F₂ — Digital

Digital (152, 200, 312)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−48, 200, 3126)-Net in Base 2 — Upper bound on s

There is no (152, 200, 3127)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 612244 174505 938504 166606 099034 628315 245898 493969 555644 526308 > 2²⁰⁰ [i]