MinT - Best Known (26, 26+17, s)-Nets in Base 2

Best Known (26, 26+17, s)-Nets in Base 2

(26, 26+17, 30)-Net over F₂ — Constructive and digital

Digital (26, 43, 30)-net over F₂, using

1 times m-reduction [i] based on digital (26, 44, 30)-net over F₂, using
- trace code for nets [i] based on digital (4, 22, 15)-net over F₄, using
  - net from sequence [i] based on digital (4, 14)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
      - an explicitly constructive algebraic function field [i]

(26, 26+17, 31)-Net over F₂ — Digital

Digital (26, 43, 31)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(26, 26+17, 132)-Net in Base 2 — Upper bound on s

There is no (26, 43, 133)-net in base 2, because

1 times m-reduction [i] would yield (26, 42, 133)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4 613114 590384 > 2⁴² [i]