MinT - Best Known (207−45, 207, s)-Nets in Base 2

Best Known (207−45, 207, s)-Nets in Base 2

(207−45, 207, 260)-Net over F₂ — Constructive and digital

Digital (162, 207, 260)-net over F₂, using

1 times m-reduction [i] based on digital (162, 208, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 52, 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]

(207−45, 207, 418)-Net over F₂ — Digital

Digital (162, 207, 418)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−45, 207, 5932)-Net in Base 2 — Upper bound on s

There is no (162, 207, 5933)-net in base 2, because

1 times m-reduction [i] would yield (162, 206, 5933)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 103 118141 754219 067669 028670 896762 474003 521473 933519 069485 295984 > 2²⁰⁶ [i]