MinT - Best Known (130−87, 130, s)-Nets in Base 8

Best Known (130−87, 130, s)-Nets in Base 8

(130−87, 130, 98)-Net over F₈ — Constructive and digital

Digital (43, 130, 98)-net over F₈, using

t-expansion [i] based on digital (37, 130, 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]

(130−87, 130, 129)-Net over F₈ — Digital

Digital (43, 130, 129)-net over F₈, using

t-expansion [i] based on digital (38, 130, 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]

(130−87, 130, 1207)-Net in Base 8 — Upper bound on s

There is no (43, 130, 1208)-net in base 8, because

1 times m-reduction [i] would yield (43, 129, 1208)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 315 635337 692958 880805 446698 203145 401149 433743 994580 290574 863288 766640 245358 562820 946672 111496 300299 325497 006557 650574 > 8¹²⁹ [i]