MinT - Best Known (38, 38+48, s)-Nets in Base 9

Best Known (38, 38+48, s)-Nets in Base 9

(38, 38+48, 81)-Net over F₉ — Constructive and digital

Digital (38, 86, 81)-net over F₉, using

t-expansion [i] based on digital (32, 86, 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]

(38, 38+48, 88)-Net in Base 9 — Constructive

(38, 86, 88)-net in base 9, using

1 times m-reduction [i] based on (38, 87, 88)-net in base 9, using
- base change [i] based on digital (9, 58, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(38, 38+48, 128)-Net over F₉ — Digital

Digital (38, 86, 128)-net over F₉, using

t-expansion [i] based on digital (33, 86, 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]

(38, 38+48, 3203)-Net in Base 9 — Upper bound on s

There is no (38, 86, 3204)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11616 499830 021586 870631 161453 846379 625764 628567 309492 336062 089047 131050 070690 624769 > 9⁸⁶ [i]