MinT - Best Known (122−60, 122, s)-Nets in Base 8

Best Known (122−60, 122, s)-Nets in Base 8

(122−60, 122, 160)-Net over F₈ — Constructive and digital

Digital (62, 122, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 61, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(122−60, 122, 219)-Net over F₈ — Digital

Digital (62, 122, 219)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−60, 122, 8076)-Net in Base 8 — Upper bound on s

There is no (62, 122, 8077)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 150 324481 324323 980959 003283 036516 991420 711299 902651 168131 392513 367156 844085 918017 264336 125097 504701 962716 034112 > 8¹²² [i]