MinT - Best Known (129−26, 129, s)-Nets in Base 2

Best Known (129−26, 129, s)-Nets in Base 2

(129−26, 129, 260)-Net over F₂ — Constructive and digital

Digital (103, 129, 260)-net over F₂, using

2¹ times duplication [i] based on digital (102, 128, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 32, 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]

(129−26, 129, 366)-Net over F₂ — Digital

Digital (103, 129, 366)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−26, 129, 5483)-Net in Base 2 — Upper bound on s

There is no (103, 129, 5484)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 681 526926 175934 862535 010633 763818 344864 > 2¹²⁹ [i]