MinT - Best Known (241−54, 241, s)-Nets in Base 2

Best Known (241−54, 241, s)-Nets in Base 2

(241−54, 241, 260)-Net over F₂ — Constructive and digital

Digital (187, 241, 260)-net over F₂, using

2¹ times duplication [i] based on digital (186, 240, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 60, 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]

(241−54, 241, 438)-Net over F₂ — Digital

Digital (187, 241, 438)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−54, 241, 5273)-Net in Base 2 — Upper bound on s

There is no (187, 241, 5274)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 540758 548420 332499 596852 094846 175692 482249 369020 109119 944565 199716 358788 > 2²⁴¹ [i]