MinT - Best Known (158−108, 158, s)-Nets in Base 8

Best Known (158−108, 158, s)-Nets in Base 8

(158−108, 158, 98)-Net over F₈ — Constructive and digital

Digital (50, 158, 98)-net over F₈, using

t-expansion [i] based on digital (37, 158, 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]

(158−108, 158, 144)-Net over F₈ — Digital

Digital (50, 158, 144)-net over F₈, using

t-expansion [i] based on digital (45, 158, 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]

(158−108, 158, 1280)-Net in Base 8 — Upper bound on s

There is no (50, 158, 1281)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 49320 206299 682700 160961 307615 169047 621734 582638 133734 544076 662335 936915 399352 207204 678907 946278 717547 881003 568767 539393 382491 606406 783844 471936 > 8¹⁵⁸ [i]