MinT - Best Known (106−67, 106, s)-Nets in Base 8

Best Known (106−67, 106, s)-Nets in Base 8

(106−67, 106, 98)-Net over F₈ — Constructive and digital

Digital (39, 106, 98)-net over F₈, using

t-expansion [i] based on digital (37, 106, 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]

(106−67, 106, 129)-Net over F₈ — Digital

Digital (39, 106, 129)-net over F₈, using

t-expansion [i] based on digital (38, 106, 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]

(106−67, 106, 1384)-Net in Base 8 — Upper bound on s

There is no (39, 106, 1385)-net in base 8, because

1 times m-reduction [i] would yield (39, 105, 1385)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 67484 539634 689879 076774 194849 366063 654323 982931 463355 133621 482302 289468 379490 877488 645798 083840 > 8¹⁰⁵ [i]