MinT - Best Known (24, 24+111, s)-Nets in Base 9

Best Known (24, 24+111, s)-Nets in Base 9

(24, 24+111, 78)-Net over F₉ — Constructive and digital

Digital (24, 135, 78)-net over F₉, using

t-expansion [i] based on digital (22, 135, 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]

(24, 24+111, 92)-Net over F₉ — Digital

Digital (24, 135, 92)-net over F₉, using

t-expansion [i] based on digital (23, 135, 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]

(24, 24+111, 530)-Net in Base 9 — Upper bound on s

There is no (24, 135, 531)-net in base 9, because

1 times m-reduction [i] would yield (24, 134, 531)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 79 273180 609686 555241 902389 928657 438333 844710 699141 630276 763440 390032 449616 194726 442458 343690 792140 387015 760013 296716 597463 954985 > 9¹³⁴ [i]