MinT - Best Known (242−46, 242, s)-Nets in Base 2

Best Known (242−46, 242, s)-Nets in Base 2

(242−46, 242, 274)-Net over F₂ — Constructive and digital

Digital (196, 242, 274)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (11, 34, 14)-net over F₂, using
  - net from sequence [i] based on digital (11, 13)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]
2. digital (162, 208, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 52, 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]

(242−46, 242, 714)-Net over F₂ — Digital

Digital (196, 242, 714)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−46, 242, 13827)-Net in Base 2 — Upper bound on s

There is no (196, 242, 13828)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 070884 413718 358037 261755 912939 302782 918473 700735 985030 657775 564742 492288 > 2²⁴² [i]