MinT - Best Known (98−57, 98, s)-Nets in Base 8

Best Known (98−57, 98, s)-Nets in Base 8

(98−57, 98, 98)-Net over F₈ — Constructive and digital

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

t-expansion [i] based on digital (37, 98, 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]

(98−57, 98, 129)-Net over F₈ — Digital

Digital (41, 98, 129)-net over F₈, using

t-expansion [i] based on digital (38, 98, 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]

(98−57, 98, 2152)-Net in Base 8 — Upper bound on s

There is no (41, 98, 2153)-net in base 8, because

1 times m-reduction [i] would yield (41, 97, 2153)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3999 776446 198708 057867 173044 895772 240062 841514 042488 269825 460196 266455 470120 799910 490520 > 8⁹⁷ [i]