MinT - Best Known (149, 149+41, s)-Nets in Base 2

Best Known (149, 149+41, s)-Nets in Base 2

(149, 149+41, 260)-Net over F₂ — Constructive and digital

Digital (149, 190, 260)-net over F₂, using

2² times duplication [i] based on digital (147, 188, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 47, 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]

(149, 149+41, 398)-Net over F₂ — Digital

Digital (149, 190, 398)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+41, 5778)-Net in Base 2 — Upper bound on s

There is no (149, 190, 5779)-net in base 2, because

1 times m-reduction [i] would yield (149, 189, 5779)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 785 332277 143121 651452 589641 965860 315257 979742 585256 595176 > 2¹⁸⁹ [i]