MinT - Best Known (147−80, 147, s)-Nets in Base 9

Best Known (147−80, 147, s)-Nets in Base 9

(147−80, 147, 165)-Net over F₉ — Constructive and digital

Digital (67, 147, 165)-net over F₉, using

t-expansion [i] based on digital (64, 147, 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]

(147−80, 147, 192)-Net over F₉ — Digital

Digital (67, 147, 192)-net over F₉, using

t-expansion [i] based on digital (61, 147, 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]

(147−80, 147, 6307)-Net in Base 9 — Upper bound on s

There is no (67, 147, 6308)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 188 315508 975451 791600 147952 646189 320877 885877 413937 360746 307198 924780 850050 477288 262320 218185 570748 668938 736253 893416 902393 203586 498307 373825 > 9¹⁴⁷ [i]