MinT - Best Known (106, 106+72, s)-Nets in Base 2

Best Known (106, 106+72, s)-Nets in Base 2

(106, 106+72, 66)-Net over F₂ — Constructive and digital

Digital (106, 178, 66)-net over F₂, using

4 times m-reduction [i] based on digital (106, 182, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 91, 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]

(106, 106+72, 82)-Net over F₂ — Digital

Digital (106, 178, 82)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+72, 388)-Net in Base 2 — Upper bound on s

There is no (106, 178, 389)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 383205 151990 649033 124966 576540 633258 321583 365930 731700 > 2¹⁷⁸ [i]