MinT - Best Known (204, 204+49, s)-Nets in Base 2

Best Known (204, 204+49, s)-Nets in Base 2

(204, 204+49, 272)-Net over F₂ — Constructive and digital

Digital (204, 253, 272)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 33, 12)-net over F₂, using
  - net from sequence [i] based on digital (9, 11)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 9 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
2. digital (171, 220, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 55, 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]

(204, 204+49, 697)-Net over F₂ — Digital

Digital (204, 253, 697)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(204, 204+49, 14160)-Net in Base 2 — Upper bound on s

There is no (204, 253, 14161)-net in base 2, because

1 times m-reduction [i] would yield (204, 252, 14161)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7237 948182 519358 713679 865119 725924 418370 749176 532664 885552 792360 552196 213064 > 2²⁵² [i]