MinT - Best Known (65, 65+79, s)-Nets in Base 9

Best Known (65, 65+79, s)-Nets in Base 9

(65, 65+79, 165)-Net over F₉ — Constructive and digital

Digital (65, 144, 165)-net over F₉, using

t-expansion [i] based on digital (64, 144, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(65, 65+79, 192)-Net over F₉ — Digital

Digital (65, 144, 192)-net over F₉, using

t-expansion [i] based on digital (61, 144, 192)-net over F₉, using
- net from sequence [i] based on digital (61, 191)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 61 and N(F) ≥ 192, using
    - Drinfeld modules of rank 1 [i]

(65, 65+79, 6046)-Net in Base 9 — Upper bound on s

There is no (65, 144, 6047)-net in base 9, because

1 times m-reduction [i] would yield (65, 143, 6047)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28684 539600 338082 933094 520612 575705 593099 418105 546169 064952 023038 074625 736730 403128 842103 683290 693669 258938 613865 424068 107798 520224 736713 > 9¹⁴³ [i]