MinT - Best Known (118−82, 118, s)-Nets in Base 8

Best Known (118−82, 118, s)-Nets in Base 8

(118−82, 118, 65)-Net over F₈ — Constructive and digital

Digital (36, 118, 65)-net over F₈, using

t-expansion [i] based on digital (14, 118, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(118−82, 118, 112)-Net over F₈ — Digital

Digital (36, 118, 112)-net over F₈, using

t-expansion [i] based on digital (35, 118, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(118−82, 118, 890)-Net in Base 8 — Upper bound on s

There is no (36, 118, 891)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 37556 896065 934389 564304 351979 985007 144058 303070 537894 564117 796456 701844 683930 578508 413548 123490 355091 415170 > 8¹¹⁸ [i]