MinT - Best Known (143−73, 143, s)-Nets in Base 9

Best Known (143−73, 143, s)-Nets in Base 9

(143−73, 143, 165)-Net over F₉ — Constructive and digital

Digital (70, 143, 165)-net over F₉, using

t-expansion [i] based on digital (64, 143, 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]

(143−73, 143, 243)-Net over F₉ — Digital

Digital (70, 143, 243)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−73, 143, 10343)-Net in Base 9 — Upper bound on s

There is no (70, 143, 10344)-net in base 9, because

1 times m-reduction [i] would yield (70, 142, 10344)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3181 903621 135901 527967 694216 862190 000570 467638 998450 736035 130789 523421 118668 242749 621623 489356 463040 174500 930067 116597 289261 601107 378945 > 9¹⁴² [i]