MinT - Best Known (154−104, 154, s)-Nets in Base 8

Best Known (154−104, 154, s)-Nets in Base 8

(154−104, 154, 98)-Net over F₈ — Constructive and digital

Digital (50, 154, 98)-net over F₈, using

t-expansion [i] based on digital (37, 154, 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]

(154−104, 154, 144)-Net over F₈ — Digital

Digital (50, 154, 144)-net over F₈, using

t-expansion [i] based on digital (45, 154, 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]

(154−104, 154, 1332)-Net in Base 8 — Upper bound on s

There is no (50, 154, 1333)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 933304 347988 148751 318823 738462 682830 893232 431732 583514 651970 912987 445261 942302 919608 661931 071310 000097 840899 525074 436446 769717 221377 477289 > 8¹⁵⁴ [i]