MinT - Best Known (158, 158+44, s)-Nets in Base 2

Best Known (158, 158+44, s)-Nets in Base 2

(158, 158+44, 260)-Net over F₂ — Constructive and digital

Digital (158, 202, 260)-net over F₂, using

2² times duplication [i] based on digital (156, 200, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 50, 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]

(158, 158+44, 407)-Net over F₂ — Digital

Digital (158, 202, 407)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+44, 5226)-Net in Base 2 — Upper bound on s

There is no (158, 202, 5227)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 454247 123388 057427 700041 715254 858565 821760 985454 004862 384868 > 2²⁰² [i]