MinT - Best Known (151−113, 151, s)-Nets in Base 8

Best Known (151−113, 151, s)-Nets in Base 8

(151−113, 151, 98)-Net over F₈ — Constructive and digital

Digital (38, 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]

(151−113, 151, 129)-Net over F₈ — Digital

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]

(151−113, 151, 778)-Net in Base 8 — Upper bound on s

There is no (38, 151, 779)-net in base 8, because

1 times m-reduction [i] would yield (38, 150, 779)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2949 558132 672803 086906 088859 604313 842066 921714 154481 660097 007678 754345 267964 192476 518386 903126 794184 969524 964287 683264 807246 339901 042832 > 8¹⁵⁰ [i]