MinT - Best Known (104−65, 104, s)-Nets in Base 8

Best Known (104−65, 104, s)-Nets in Base 8

(104−65, 104, 98)-Net over F₈ — Constructive and digital

Digital (39, 104, 98)-net over F₈, using

t-expansion [i] based on digital (37, 104, 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]

(104−65, 104, 129)-Net over F₈ — Digital

Digital (39, 104, 129)-net over F₈, using

t-expansion [i] based on digital (38, 104, 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]

(104−65, 104, 1454)-Net in Base 8 — Upper bound on s

There is no (39, 104, 1455)-net in base 8, because

1 times m-reduction [i] would yield (39, 103, 1455)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1057 299608 494101 137634 581857 410376 494632 986598 325846 268046 591515 369867 735481 736945 338085 213177 > 8¹⁰³ [i]