MinT - Best Known (129−82, 129, s)-Nets in Base 8

Best Known (129−82, 129, s)-Nets in Base 8

(129−82, 129, 98)-Net over F₈ — Constructive and digital

Digital (47, 129, 98)-net over F₈, using

t-expansion [i] based on digital (37, 129, 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]

(129−82, 129, 144)-Net over F₈ — Digital

Digital (47, 129, 144)-net over F₈, using

t-expansion [i] based on digital (45, 129, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(129−82, 129, 1574)-Net in Base 8 — Upper bound on s

There is no (47, 129, 1575)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 317 423645 456527 078182 454742 508995 171905 922027 894508 810431 203944 908245 655427 604440 358222 160694 745773 229535 540651 271552 > 8¹²⁹ [i]