MinT - Best Known (101−58, 101, s)-Nets in Base 8

Best Known (101−58, 101, s)-Nets in Base 8

(101−58, 101, 98)-Net over F₈ — Constructive and digital

Digital (43, 101, 98)-net over F₈, using

t-expansion [i] based on digital (37, 101, 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]

(101−58, 101, 129)-Net over F₈ — Digital

Digital (43, 101, 129)-net over F₈, using

t-expansion [i] based on digital (38, 101, 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]

(101−58, 101, 2311)-Net in Base 8 — Upper bound on s

There is no (43, 101, 2312)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 16 412095 333235 463048 312378 578317 884407 976936 708042 418852 606260 896987 334210 758782 036116 888864 > 8¹⁰¹ [i]