MinT - Best Known (210, 260, s)-Nets in Base 2

Best Known (210, 260, s)-Nets in Base 2

(210, 260, 274)-Net over F₂ — Constructive and digital

Digital (210, 260, 274)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (11, 36, 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 (174, 224, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 56, 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]

(210, 260, 729)-Net over F₂ — Digital

Digital (210, 260, 729)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(210, 260, 13714)-Net in Base 2 — Upper bound on s

There is no (210, 260, 13715)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 855517 400291 363112 337850 794426 328938 093622 576124 497820 199232 684950 838022 985280 > 2²⁶⁰ [i]