MinT - Best Known (198−43, 198, s)-Nets in Base 2

Best Known (198−43, 198, s)-Nets in Base 2

(198−43, 198, 260)-Net over F₂ — Constructive and digital

Digital (155, 198, 260)-net over F₂, using

2² times duplication [i] based on digital (153, 196, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 49, 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]

(198−43, 198, 404)-Net over F₂ — Digital

Digital (155, 198, 404)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−43, 198, 5755)-Net in Base 2 — Upper bound on s

There is no (155, 198, 5756)-net in base 2, because

1 times m-reduction [i] would yield (155, 197, 5756)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 200937 140517 891089 979809 806679 782290 020539 348909 415276 251746 > 2¹⁹⁷ [i]