MinT - Best Known (118−72, 118, s)-Nets in Base 9

Best Known (118−72, 118, s)-Nets in Base 9

(118−72, 118, 81)-Net over F₉ — Constructive and digital

Digital (46, 118, 81)-net over F₉, using

t-expansion [i] based on digital (32, 118, 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]

(118−72, 118, 162)-Net over F₉ — Digital

Digital (46, 118, 162)-net over F₉, using

net from sequence [i] based on digital (46, 161)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(118−72, 118, 2373)-Net in Base 9 — Upper bound on s

There is no (46, 118, 2374)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39980 005480 466602 121765 454115 209407 332709 409682 051717 564811 723675 163189 484911 706572 602351 829297 744064 483431 459393 > 9¹¹⁸ [i]