MinT - Best Known (66, 66+69, s)-Nets in Base 9

Best Known (66, 66+69, s)-Nets in Base 9

(66, 66+69, 165)-Net over F₉ — Constructive and digital

Digital (66, 135, 165)-net over F₉, using

t-expansion [i] based on digital (64, 135, 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]

(66, 66+69, 230)-Net over F₉ — Digital

Digital (66, 135, 230)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+69, 9734)-Net in Base 9 — Upper bound on s

There is no (66, 135, 9735)-net in base 9, because

1 times m-reduction [i] would yield (66, 134, 9735)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 74 086280 651885 177696 036372 331283 165379 035221 281034 582381 786526 967688 282351 068635 564741 864435 114429 266377 860633 706534 867741 638257 > 9¹³⁴ [i]