MinT - Best Known (166−123, 166, s)-Nets in Base 8

Best Known (166−123, 166, s)-Nets in Base 8

(166−123, 166, 98)-Net over F₈ — Constructive and digital

Digital (43, 166, 98)-net over F₈, using

t-expansion [i] based on digital (37, 166, 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]

(166−123, 166, 129)-Net over F₈ — Digital

Digital (43, 166, 129)-net over F₈, using

t-expansion [i] based on digital (38, 166, 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]

(166−123, 166, 894)-Net in Base 8 — Upper bound on s

There is no (43, 166, 895)-net in base 8, because

1 times m-reduction [i] would yield (43, 165, 895)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 103506 562800 662583 659498 801354 460823 945803 271374 282521 403158 914711 585452 267518 515458 677850 569123 264620 977874 278480 644784 596421 464342 786040 079339 516078 > 8¹⁶⁵ [i]