MinT - Best Known (120−32, 120, s)-Nets in Base 8

Best Known (120−32, 120, s)-Nets in Base 8

(120−32, 120, 1026)-Net over F₈ — Constructive and digital

Digital (88, 120, 1026)-net over F₈, using

trace code for nets [i] based on digital (28, 60, 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]

(120−32, 120, 5571)-Net over F₈ — Digital

Digital (88, 120, 5571)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−32, 120, 5762551)-Net in Base 8 — Upper bound on s

There is no (88, 120, 5762552)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 348543 262460 947743 052928 806735 013201 535535 241199 792001 247007 034507 688117 225563 246364 762189 112231 142250 166415 > 8¹²⁰ [i]