MinT - Best Known (147−77, 147, s)-Nets in Base 9

Best Known (147−77, 147, s)-Nets in Base 9

(147−77, 147, 165)-Net over F₉ — Constructive and digital

Digital (70, 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]

(147−77, 147, 224)-Net over F₉ — Digital

Digital (70, 147, 224)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−77, 147, 8686)-Net in Base 9 — Upper bound on s

There is no (70, 147, 8687)-net in base 9, because

1 times m-reduction [i] would yield (70, 146, 8687)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 894311 184853 173630 081803 879153 896877 752088 234996 834475 701312 949869 575594 626469 473713 668377 169468 080595 090971 559740 287690 098263 167550 024145 > 9¹⁴⁶ [i]