MinT - Best Known (116−72, 116, s)-Nets in Base 9

Best Known (116−72, 116, s)-Nets in Base 9

(116−72, 116, 81)-Net over F₉ — Constructive and digital

Digital (44, 116, 81)-net over F₉, using

t-expansion [i] based on digital (32, 116, 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]

(116−72, 116, 147)-Net over F₉ — Digital

Digital (44, 116, 147)-net over F₉, using

t-expansion [i] based on digital (43, 116, 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]

(116−72, 116, 2098)-Net in Base 9 — Upper bound on s

There is no (44, 116, 2099)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 496 220883 354923 375550 802189 924793 227441 366561 984960 023700 817028 030997 077106 567820 891715 768780 093863 071216 092769 > 9¹¹⁶ [i]