MinT - Best Known (101−65, 101, s)-Nets in Base 9

Best Known (101−65, 101, s)-Nets in Base 9

(101−65, 101, 81)-Net over F₉ — Constructive and digital

Digital (36, 101, 81)-net over F₉, using

t-expansion [i] based on digital (32, 101, 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]

(101−65, 101, 128)-Net over F₉ — Digital

Digital (36, 101, 128)-net over F₉, using

t-expansion [i] based on digital (33, 101, 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]

(101−65, 101, 1514)-Net in Base 9 — Upper bound on s

There is no (36, 101, 1515)-net in base 9, because

1 times m-reduction [i] would yield (36, 100, 1515)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 268527 294123 524103 440027 611482 230803 918071 340423 491196 000044 640661 569046 898233 441643 073622 614785 > 9¹⁰⁰ [i]