MinT - Best Known (123−79, 123, s)-Nets in Base 9

Best Known (123−79, 123, s)-Nets in Base 9

(123−79, 123, 81)-Net over F₉ — Constructive and digital

Digital (44, 123, 81)-net over F₉, using

t-expansion [i] based on digital (32, 123, 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]

(123−79, 123, 147)-Net over F₉ — Digital

Digital (44, 123, 147)-net over F₉, using

t-expansion [i] based on digital (43, 123, 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]

(123−79, 123, 1835)-Net in Base 9 — Upper bound on s

There is no (44, 123, 1836)-net in base 9, because

1 times m-reduction [i] would yield (44, 122, 1836)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 263 011488 594944 215271 870064 431074 158612 238901 501511 802443 321044 694931 118235 386960 314066 704567 894904 857413 319377 206049 > 9¹²² [i]