MinT - Best Known (147−79, 147, s)-Nets in Base 9

Best Known (147−79, 147, s)-Nets in Base 9

(147−79, 147, 165)-Net over F₉ — Constructive and digital

Digital (68, 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]

(147−79, 147, 201)-Net over F₉ — Digital

Digital (68, 147, 201)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−79, 147, 7164)-Net in Base 9 — Upper bound on s

There is no (68, 147, 7165)-net in base 9, because

1 times m-reduction [i] would yield (68, 146, 7165)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 924058 969717 328880 158202 301481 609177 653505 720036 789360 238197 103282 327765 128768 878805 684019 956262 012069 646756 006173 141137 120201 137423 213081 > 9¹⁴⁶ [i]