MinT - Best Known (103, 130, s)-Nets in Base 2

Best Known (103, 130, s)-Nets in Base 2

(103, 130, 196)-Net over F₂ — Constructive and digital

Digital (103, 130, 196)-net over F₂, using

2² times duplication [i] based on digital (101, 128, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 32, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(103, 130, 334)-Net over F₂ — Digital

Digital (103, 130, 334)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 130, 5483)-Net in Base 2 — Upper bound on s

There is no (103, 130, 5484)-net in base 2, because

1 times m-reduction [i] would yield (103, 129, 5484)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 681 526926 175934 862535 010633 763818 344864 > 2¹²⁹ [i]