MinT - Best Known (43, 43+100, s)-Nets in Base 9

Best Known (43, 43+100, s)-Nets in Base 9

(43, 43+100, 81)-Net over F₉ — Constructive and digital

Digital (43, 143, 81)-net over F₉, using

t-expansion [i] based on digital (32, 143, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(43, 43+100, 147)-Net over F₉ — Digital

Digital (43, 143, 147)-net over F₉, using

net from sequence [i] based on digital (43, 146)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
  - a curve from the manYPoints database [i]

(43, 43+100, 1274)-Net in Base 9 — Upper bound on s

There is no (43, 143, 1275)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28902 683163 624944 411904 898220 846098 147700 607278 295991 679450 334277 299414 511295 149423 664887 375614 825769 352515 594668 389163 434003 707935 235761 > 9¹⁴³ [i]