MinT - Best Known (177, 177+51, s)-Nets in Base 2

Best Known (177, 177+51, s)-Nets in Base 2

(177, 177+51, 260)-Net over F₂ — Constructive and digital

Digital (177, 228, 260)-net over F₂, using

trace code for nets [i] based on digital (6, 57, 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]

(177, 177+51, 419)-Net over F₂ — Digital

Digital (177, 228, 419)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(177, 177+51, 5470)-Net in Base 2 — Upper bound on s

There is no (177, 228, 5471)-net in base 2, because

1 times m-reduction [i] would yield (177, 227, 5471)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 215 764237 199239 384834 644434 361415 803823 703681 527943 104228 736698 956120 > 2²²⁷ [i]