MinT - Best Known (68, 149, s)-Nets in Base 9

Best Known (68, 149, s)-Nets in Base 9

(68, 149, 165)-Net over F₉ — Constructive and digital

Digital (68, 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]

(68, 149, 194)-Net over F₉ — Digital

Digital (68, 149, 194)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 149, 6665)-Net in Base 9 — Upper bound on s

There is no (68, 149, 6666)-net in base 9, because

1 times m-reduction [i] would yield (68, 148, 6666)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1699 139705 911750 093507 660204 274154 805410 854005 661426 566288 162352 770792 207799 635539 606109 077199 849601 018635 397532 594878 013520 019831 883560 997249 > 9¹⁴⁸ [i]