MinT - Best Known (66, 66+84, s)-Nets in Base 9

Best Known (66, 66+84, s)-Nets in Base 9

(66, 66+84, 165)-Net over F₉ — Constructive and digital

Digital (66, 150, 165)-net over F₉, using

t-expansion [i] based on digital (64, 150, 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+84, 192)-Net over F₉ — Digital

Digital (66, 150, 192)-net over F₉, using

t-expansion [i] based on digital (61, 150, 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+84, 5255)-Net in Base 9 — Upper bound on s

There is no (66, 150, 5256)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 137607 976781 108505 508198 686008 641143 051561 543724 942911 049680 457695 438457 570411 006878 489501 739727 522958 894758 417716 637761 615116 796279 658570 532737 > 9¹⁵⁰ [i]