MinT - Best Known (202−83, 202, s)-Nets in Base 2

Best Known (202−83, 202, s)-Nets in Base 2

(202−83, 202, 66)-Net over F₂ — Constructive and digital

Digital (119, 202, 66)-net over F₂, using

6 times m-reduction [i] based on digital (119, 208, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 104, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(202−83, 202, 88)-Net over F₂ — Digital

Digital (119, 202, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−83, 202, 425)-Net in Base 2 — Upper bound on s

There is no (119, 202, 426)-net in base 2, because

1 times m-reduction [i] would yield (119, 201, 426)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 495160 024656 512943 247044 857767 863819 233125 088847 295407 947359 > 2²⁰¹ [i]