MinT - Best Known (72, 72+77, s)-Nets in Base 9

Best Known (72, 72+77, s)-Nets in Base 9

(72, 72+77, 165)-Net over F₉ — Constructive and digital

Digital (72, 149, 165)-net over F₉, using

t-expansion [i] based on digital (64, 149, 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, 72+77, 239)-Net over F₉ — Digital

Digital (72, 149, 239)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+77, 9754)-Net in Base 9 — Upper bound on s

There is no (72, 149, 9755)-net in base 9, because

1 times m-reduction [i] would yield (72, 148, 9755)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1693 537484 830103 392114 921876 781485 776874 979564 588470 743823 780147 699015 357683 279269 624355 095628 817932 360172 358421 754449 333538 152479 440250 380689 > 9¹⁴⁸ [i]