MinT - Best Known (172, 215, s)-Nets in Base 2

Best Known (172, 215, s)-Nets in Base 2

(172, 215, 260)-Net over F₂ — Constructive and digital

Digital (172, 215, 260)-net over F₂, using

t-expansion [i] based on digital (171, 215, 260)-net over F₂, using
- 5 times m-reduction [i] based on digital (171, 220, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 55, 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]

(172, 215, 551)-Net over F₂ — Digital

Digital (172, 215, 551)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 215, 10111)-Net in Base 2 — Upper bound on s

There is no (172, 215, 10112)-net in base 2, because

1 times m-reduction [i] would yield (172, 214, 10112)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26370 127847 103875 766234 004301 431919 556380 346577 623424 247596 839417 > 2²¹⁴ [i]