MinT - Best Known (98−65, 98, s)-Nets in Base 9

Best Known (98−65, 98, s)-Nets in Base 9

(98−65, 98, 81)-Net over F₉ — Constructive and digital

Digital (33, 98, 81)-net over F₉, using

t-expansion [i] based on digital (32, 98, 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]

(98−65, 98, 128)-Net over F₉ — Digital

Digital (33, 98, 128)-net over F₉, using

net from sequence [i] based on digital (33, 127)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
  - a curve from the manYPoints database [i]

(98−65, 98, 1228)-Net in Base 9 — Upper bound on s

There is no (33, 98, 1229)-net in base 9, because

1 times m-reduction [i] would yield (33, 97, 1229)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 364 876136 153078 989423 216244 127328 792589 565550 353855 129513 580876 229138 069956 146300 137627 558145 > 9⁹⁷ [i]