MinT - Best Known (113−72, 113, s)-Nets in Base 8

Best Known (113−72, 113, s)-Nets in Base 8

(113−72, 113, 98)-Net over F₈ — Constructive and digital

Digital (41, 113, 98)-net over F₈, using

t-expansion [i] based on digital (37, 113, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(113−72, 113, 129)-Net over F₈ — Digital

Digital (41, 113, 129)-net over F₈, using

t-expansion [i] based on digital (38, 113, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(113−72, 113, 1371)-Net in Base 8 — Upper bound on s

There is no (41, 113, 1372)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 128263 100543 408753 147725 419633 743050 774703 331106 997111 175544 558181 247772 487364 775428 224605 366012 338060 > 8¹¹³ [i]