MinT - Best Known (145−30, 145, s)-Nets in Base 2

Best Known (145−30, 145, s)-Nets in Base 2

(145−30, 145, 260)-Net over F₂ — Constructive and digital

Digital (115, 145, 260)-net over F₂, using

2¹ times duplication [i] based on digital (114, 144, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 36, 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]

(145−30, 145, 365)-Net over F₂ — Digital

Digital (115, 145, 365)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−30, 145, 5198)-Net in Base 2 — Upper bound on s

There is no (115, 145, 5199)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 44 643012 581526 251408 221235 412501 498975 370446 > 2¹⁴⁵ [i]