MinT - Best Known (144−101, 144, s)-Nets in Base 8

Best Known (144−101, 144, s)-Nets in Base 8

(144−101, 144, 98)-Net over F₈ — Constructive and digital

Digital (43, 144, 98)-net over F₈, using

t-expansion [i] based on digital (37, 144, 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]

(144−101, 144, 129)-Net over F₈ — Digital

Digital (43, 144, 129)-net over F₈, using

t-expansion [i] based on digital (38, 144, 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]

(144−101, 144, 1033)-Net in Base 8 — Upper bound on s

There is no (43, 144, 1034)-net in base 8, because

1 times m-reduction [i] would yield (43, 143, 1034)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1401 732842 912827 261437 498028 855405 263386 725679 306406 145994 014214 042427 727948 214046 079842 904856 724856 695632 468836 575806 592196 695296 > 8¹⁴³ [i]