MinT - Best Known (147−103, 147, s)-Nets in Base 9

Best Known (147−103, 147, s)-Nets in Base 9

(147−103, 147, 81)-Net over F₉ — Constructive and digital

Digital (44, 147, 81)-net over F₉, using

t-expansion [i] based on digital (32, 147, 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]

(147−103, 147, 147)-Net over F₉ — Digital

Digital (44, 147, 147)-net over F₉, using

t-expansion [i] based on digital (43, 147, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(147−103, 147, 1307)-Net in Base 9 — Upper bound on s

There is no (44, 147, 1308)-net in base 9, because

1 times m-reduction [i] would yield (44, 146, 1308)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 648950 145960 669769 742500 457514 600623 098938 555543 173769 462225 340491 140530 208307 043206 111521 398747 585118 920203 705842 953848 533161 027140 141345 > 9¹⁴⁶ [i]