MinT - Best Known (66, 66+79, s)-Nets in Base 9

Best Known (66, 66+79, s)-Nets in Base 9

(66, 66+79, 165)-Net over F₉ — Constructive and digital

Digital (66, 145, 165)-net over F₉, using

t-expansion [i] based on digital (64, 145, 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]

(66, 66+79, 192)-Net over F₉ — Digital

Digital (66, 145, 192)-net over F₉, using

t-expansion [i] based on digital (61, 145, 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]

(66, 66+79, 6398)-Net in Base 9 — Upper bound on s

There is no (66, 145, 6399)-net in base 9, because

1 times m-reduction [i] would yield (66, 144, 6399)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 258407 468560 735944 898756 502187 865706 828575 969960 552383 534412 820615 052246 000916 739931 733792 294292 568916 576157 784188 419116 056107 114924 725961 > 9¹⁴⁴ [i]