MinT - Best Known (136−40, 136, s)-Nets in Base 8

Best Known (136−40, 136, s)-Nets in Base 8

(136−40, 136, 1026)-Net over F₈ — Constructive and digital

Digital (96, 136, 1026)-net over F₈, using

trace code for nets [i] based on digital (28, 68, 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]

(136−40, 136, 3121)-Net over F₈ — Digital

Digital (96, 136, 3121)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−40, 136, 1641409)-Net in Base 8 — Upper bound on s

There is no (96, 136, 1641410)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 661 063338 795538 457204 169955 721305 261429 437783 958596 454952 194981 212743 550155 557986 899151 161467 904391 553517 543775 272752 616912 > 8¹³⁶ [i]