MinT - Best Known (149−110, 149, s)-Nets in Base 8

Best Known (149−110, 149, s)-Nets in Base 8

(149−110, 149, 98)-Net over F₈ — Constructive and digital

Digital (39, 149, 98)-net over F₈, using

t-expansion [i] based on digital (37, 149, 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]

(149−110, 149, 129)-Net over F₈ — Digital

Digital (39, 149, 129)-net over F₈, using

t-expansion [i] based on digital (38, 149, 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]

(149−110, 149, 817)-Net in Base 8 — Upper bound on s

There is no (39, 149, 818)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 365 597854 430750 393098 324234 870026 343778 377000 525657 688446 420168 499835 426050 153481 820421 106342 791905 981897 280515 445087 853421 662196 215168 > 8¹⁴⁹ [i]