MinT - Best Known (113−70, 113, s)-Nets in Base 9

Best Known (113−70, 113, s)-Nets in Base 9

(113−70, 113, 81)-Net over F₉ — Constructive and digital

Digital (43, 113, 81)-net over F₉, using

t-expansion [i] based on digital (32, 113, 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]

(113−70, 113, 147)-Net over F₉ — Digital

Digital (43, 113, 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]

(113−70, 113, 2072)-Net in Base 9 — Upper bound on s

There is no (43, 113, 2073)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 676639 990555 018205 538759 274348 171561 352238 716970 869907 966624 389119 834939 885563 057863 284363 108667 847477 013785 > 9¹¹³ [i]