MinT - Best Known (129−93, 129, s)-Nets in Base 9

Best Known (129−93, 129, s)-Nets in Base 9

(129−93, 129, 81)-Net over F₉ — Constructive and digital

Digital (36, 129, 81)-net over F₉, using

t-expansion [i] based on digital (32, 129, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(129−93, 129, 128)-Net over F₉ — Digital

Digital (36, 129, 128)-net over F₉, using

t-expansion [i] based on digital (33, 129, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(129−93, 129, 989)-Net in Base 9 — Upper bound on s

There is no (36, 129, 990)-net in base 9, because

1 times m-reduction [i] would yield (36, 128, 990)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 144 018544 180254 478554 035312 715587 940615 493607 577153 443384 246784 486643 318956 856745 740072 979829 681365 071741 792567 195795 297761 > 9¹²⁸ [i]