MinT - Best Known (71, 71+71, s)-Nets in Base 9

Best Known (71, 71+71, s)-Nets in Base 9

(71, 71+71, 165)-Net over F₉ — Constructive and digital

Digital (71, 142, 165)-net over F₉, using

t-expansion [i] based on digital (64, 142, 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]

(71, 71+71, 264)-Net over F₉ — Digital

Digital (71, 142, 264)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+71, 12123)-Net in Base 9 — Upper bound on s

There is no (71, 142, 12124)-net in base 9, because

1 times m-reduction [i] would yield (71, 141, 12124)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 353 415448 791246 166052 501499 080748 342488 678934 468785 768071 724275 226895 449860 029342 059393 809009 143828 822922 006708 973661 719536 635479 156001 > 9¹⁴¹ [i]