MinT - Best Known (131−97, 131, s)-Nets in Base 9

Best Known (131−97, 131, s)-Nets in Base 9

(131−97, 131, 81)-Net over F₉ — Constructive and digital

Digital (34, 131, 81)-net over F₉, using

t-expansion [i] based on digital (32, 131, 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]

(131−97, 131, 128)-Net over F₉ — Digital

Digital (34, 131, 128)-net over F₉, using

t-expansion [i] based on digital (33, 131, 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]

(131−97, 131, 870)-Net in Base 9 — Upper bound on s

There is no (34, 131, 871)-net in base 9, because

1 times m-reduction [i] would yield (34, 130, 871)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11565 534192 474484 267685 545776 815232 214003 826237 356761 399593 811128 613311 702766 353249 282934 046618 046575 844608 104985 906015 572609 > 9¹³⁰ [i]