MinT - Best Known (188−41, 188, s)-Nets in Base 2

Best Known (188−41, 188, s)-Nets in Base 2

(188−41, 188, 260)-Net over F₂ — Constructive and digital

Digital (147, 188, 260)-net over F₂, using

trace code for nets [i] based on digital (6, 47, 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]

(188−41, 188, 383)-Net over F₂ — Digital

Digital (147, 188, 383)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−41, 188, 5389)-Net in Base 2 — Upper bound on s

There is no (147, 188, 5390)-net in base 2, because

1 times m-reduction [i] would yield (147, 187, 5390)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 196 310202 244909 600771 904211 571658 497342 548002 739445 368304 > 2¹⁸⁷ [i]