MinT - Best Known (258−53, 258, s)-Nets in Base 2

Best Known (258−53, 258, s)-Nets in Base 2

(258−53, 258, 260)-Net over F₂ — Constructive and digital

Digital (205, 258, 260)-net over F₂, using

t-expansion [i] based on digital (201, 258, 260)-net over F₂, using
- 2 times m-reduction [i] based on digital (201, 260, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 65, 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]

(258−53, 258, 592)-Net over F₂ — Digital

Digital (205, 258, 592)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−53, 258, 9935)-Net in Base 2 — Upper bound on s

There is no (205, 258, 9936)-net in base 2, because

1 times m-reduction [i] would yield (205, 257, 9936)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 231992 362194 486413 487584 618775 441399 923627 377238 139048 509520 833688 463696 285108 > 2²⁵⁷ [i]