MinT - Best Known (147−73, 147, s)-Nets in Base 9

Best Known (147−73, 147, s)-Nets in Base 9

(147−73, 147, 165)-Net over F₉ — Constructive and digital

Digital (74, 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]

(147−73, 147, 280)-Net over F₉ — Digital

Digital (74, 147, 280)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−73, 147, 13210)-Net in Base 9 — Upper bound on s

There is no (74, 147, 13211)-net in base 9, because

1 times m-reduction [i] would yield (74, 146, 13211)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 911775 768914 725039 090673 198022 316214 471697 434403 261276 266194 438033 934820 170048 781915 471469 263487 884970 839981 590896 984622 698434 727644 167521 > 9¹⁴⁶ [i]