MinT - Best Known (124−81, 124, s)-Nets in Base 8

Best Known (124−81, 124, s)-Nets in Base 8

(124−81, 124, 98)-Net over F₈ — Constructive and digital

Digital (43, 124, 98)-net over F₈, using

t-expansion [i] based on digital (37, 124, 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]

(124−81, 124, 129)-Net over F₈ — Digital

Digital (43, 124, 129)-net over F₈, using

t-expansion [i] based on digital (38, 124, 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]

(124−81, 124, 1322)-Net in Base 8 — Upper bound on s

There is no (43, 124, 1323)-net in base 8, because

1 times m-reduction [i] would yield (43, 123, 1323)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1204 464146 885804 352373 505220 736095 729118 675405 873534 075385 766524 126367 970101 373954 234026 994400 173608 094827 299477 > 8¹²³ [i]