MinT - Best Known (151−108, 151, s)-Nets in Base 8

Best Known (151−108, 151, s)-Nets in Base 8

(151−108, 151, 98)-Net over F₈ — Constructive and digital

Digital (43, 151, 98)-net over F₈, using

t-expansion [i] based on digital (37, 151, 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]

(151−108, 151, 129)-Net over F₈ — Digital

Digital (43, 151, 129)-net over F₈, using

t-expansion [i] based on digital (38, 151, 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]

(151−108, 151, 970)-Net in Base 8 — Upper bound on s

There is no (43, 151, 971)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 24311 649599 612808 154528 509072 031162 444090 240155 575217 622452 730802 510738 715241 592570 589362 172533 705185 117803 890763 582915 201134 450387 615272 > 8¹⁵¹ [i]