MinT - Best Known (144−95, 144, s)-Nets in Base 9

Best Known (144−95, 144, s)-Nets in Base 9

(144−95, 144, 81)-Net over F₉ — Constructive and digital

Digital (49, 144, 81)-net over F₉, using

t-expansion [i] based on digital (32, 144, 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]

(144−95, 144, 168)-Net over F₉ — Digital

Digital (49, 144, 168)-net over F₉, using

net from sequence [i] based on digital (49, 167)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 49 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(144−95, 144, 1809)-Net in Base 9 — Upper bound on s

There is no (49, 144, 1810)-net in base 9, because

1 times m-reduction [i] would yield (49, 143, 1810)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29177 745565 259291 252807 488980 039232 068793 136342 519831 110525 031454 044177 144226 126321 413301 552061 204645 937630 419876 763202 444399 877523 238705 > 9¹⁴³ [i]