MinT - Best Known (48, 48+93, s)-Nets in Base 9

Best Known (48, 48+93, s)-Nets in Base 9

(48, 48+93, 81)-Net over F₉ — Constructive and digital

Digital (48, 141, 81)-net over F₉, using

t-expansion [i] based on digital (32, 141, 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]

(48, 48+93, 163)-Net over F₉ — Digital

Digital (48, 141, 163)-net over F₉, using

net from sequence [i] based on digital (48, 162)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 48 and N(F) ≥ 163, using
  - Drinfeld modules of rank 1 [i]

(48, 48+93, 1776)-Net in Base 9 — Upper bound on s

There is no (48, 141, 1777)-net in base 9, because

1 times m-reduction [i] would yield (48, 140, 1777)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 890027 083998 953427 541010 257195 644740 907697 460182 497682 369667 232549 859987 728429 464161 178000 670563 238913 776011 468665 239197 980158 206769 > 9¹⁴⁰ [i]