MinT - Best Known (171−129, 171, s)-Nets in Base 8

Best Known (171−129, 171, s)-Nets in Base 8

(171−129, 171, 98)-Net over F₈ — Constructive and digital

Digital (42, 171, 98)-net over F₈, using

t-expansion [i] based on digital (37, 171, 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]

(171−129, 171, 129)-Net over F₈ — Digital

Digital (42, 171, 129)-net over F₈, using

t-expansion [i] based on digital (38, 171, 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]

(171−129, 171, 842)-Net in Base 8 — Upper bound on s

There is no (42, 171, 843)-net in base 8, because

1 times m-reduction [i] would yield (42, 170, 843)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3365 913617 196666 682440 525074 839400 930167 951354 164668 966561 168718 343427 539163 250469 567959 030946 883166 044483 440583 033945 111309 877724 925944 057120 949068 035421 > 8¹⁷⁰ [i]