MinT - Best Known (156−50, 156, s)-Nets in Base 8

Best Known (156−50, 156, s)-Nets in Base 8

(156−50, 156, 1026)-Net over F₈ — Constructive and digital

Digital (106, 156, 1026)-net over F₈, using

trace code for nets [i] based on digital (28, 78, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(156−50, 156, 2073)-Net over F₈ — Digital

Digital (106, 156, 2073)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−50, 156, 627767)-Net in Base 8 — Upper bound on s

There is no (106, 156, 627768)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 762 173735 978299 210419 178627 201818 855476 554189 308114 418391 347614 563668 856771 257787 499665 336164 444890 981559 001101 527880 338747 713348 290445 769428 > 8¹⁵⁶ [i]