MinT - Best Known (43, 145, s)-Nets in Base 8

Best Known (43, 145, s)-Nets in Base 8

(43, 145, 98)-Net over F₈ — Constructive and digital

Digital (43, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 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]

(43, 145, 129)-Net over F₈ — Digital

Digital (43, 145, 129)-net over F₈, using

t-expansion [i] based on digital (38, 145, 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]

(43, 145, 1016)-Net in Base 8 — Upper bound on s

There is no (43, 145, 1017)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 93035 489938 206639 901781 505004 865607 728385 819662 856375 748582 581271 945094 232919 759239 505429 439731 974222 225569 502844 316887 383552 422280 > 8¹⁴⁵ [i]