MinT - Best Known (72, 147, s)-Nets in Base 9

Best Known (72, 147, s)-Nets in Base 9

(72, 147, 165)-Net over F₉ — Constructive and digital

Digital (72, 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]

(72, 147, 249)-Net over F₉ — Digital

Digital (72, 147, 249)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 147, 10648)-Net in Base 9 — Upper bound on s

There is no (72, 147, 10649)-net in base 9, because

1 times m-reduction [i] would yield (72, 146, 10649)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 897867 413394 018094 294030 884960 934600 973378 554136 742909 200778 244754 598532 915883 128774 499082 066597 822262 751610 558385 098173 985453 452916 829545 > 9¹⁴⁶ [i]