MinT - Best Known (105−67, 105, s)-Nets in Base 8

Best Known (105−67, 105, s)-Nets in Base 8

(105−67, 105, 98)-Net over F₈ — Constructive and digital

Digital (38, 105, 98)-net over F₈, using

t-expansion [i] based on digital (37, 105, 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]

(105−67, 105, 129)-Net over F₈ — Digital

Digital (38, 105, 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]

(105−67, 105, 1298)-Net in Base 8 — Upper bound on s

There is no (38, 105, 1299)-net in base 8, because

1 times m-reduction [i] would yield (38, 104, 1299)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8400 622075 694759 452002 075972 317898 378221 481016 249683 393677 278387 515501 074726 768755 802279 322800 > 8¹⁰⁴ [i]