MinT - Best Known (141−117, 141, s)-Nets in Base 9

Best Known (141−117, 141, s)-Nets in Base 9

(141−117, 141, 78)-Net over F₉ — Constructive and digital

Digital (24, 141, 78)-net over F₉, using

t-expansion [i] based on digital (22, 141, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(141−117, 141, 92)-Net over F₉ — Digital

Digital (24, 141, 92)-net over F₉, using

t-expansion [i] based on digital (23, 141, 92)-net over F₉, using
- net from sequence [i] based on digital (23, 91)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 23 and N(F) ≥ 92, using
    - Drinfeld modules of rank 1 [i]

(141−117, 141, 529)-Net in Base 9 — Upper bound on s

There is no (24, 141, 530)-net in base 9, because

1 times m-reduction [i] would yield (24, 140, 530)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 42 817112 192508 671859 327618 099413 209817 625425 673765 796728 149046 386230 941734 436598 382332 412933 926363 437518 981646 390837 605467 083376 306785 > 9¹⁴⁰ [i]