MinT - Best Known (207−87, 207, s)-Nets in Base 2

Best Known (207−87, 207, s)-Nets in Base 2

(207−87, 207, 66)-Net over F₂ — Constructive and digital

Digital (120, 207, 66)-net over F₂, using

3 times m-reduction [i] based on digital (120, 210, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 105, 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]

(207−87, 207, 85)-Net over F₂ — Digital

Digital (120, 207, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−87, 207, 407)-Net in Base 2 — Upper bound on s

There is no (120, 207, 408)-net in base 2, because

1 times m-reduction [i] would yield (120, 206, 408)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 112 312942 003526 098417 626654 300700 574695 708103 400837 439264 011880 > 2²⁰⁶ [i]