MinT - Best Known (123−85, 123, s)-Nets in Base 8

Best Known (123−85, 123, s)-Nets in Base 8

(123−85, 123, 98)-Net over F₈ — Constructive and digital

Digital (38, 123, 98)-net over F₈, using

t-expansion [i] based on digital (37, 123, 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]

(123−85, 123, 129)-Net over F₈ — Digital

Digital (38, 123, 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]

(123−85, 123, 964)-Net in Base 8 — Upper bound on s

There is no (38, 123, 965)-net in base 8, because

1 times m-reduction [i] would yield (38, 122, 965)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 153 746495 914117 288586 151655 456224 818061 647892 981595 979612 915725 181501 176930 129943 619323 060180 225325 802472 016784 > 8¹²² [i]