MinT - Best Known (148−117, 148, s)-Nets in Base 9

Best Known (148−117, 148, s)-Nets in Base 9

(148−117, 148, 78)-Net over F₉ — Constructive and digital

Digital (31, 148, 78)-net over F₉, using

t-expansion [i] based on digital (22, 148, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(148−117, 148, 120)-Net over F₉ — Digital

Digital (31, 148, 120)-net over F₉, using

net from sequence [i] based on digital (31, 119)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
  - a curve from the manYPoints database [i]

(148−117, 148, 700)-Net in Base 9 — Upper bound on s

There is no (31, 148, 701)-net in base 9, because

1 times m-reduction [i] would yield (31, 147, 701)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 197 531694 603154 476360 353637 410229 581417 739421 218880 002967 135945 114915 438385 463383 066972 602230 524463 785935 810405 495436 693146 312389 491769 583185 > 9¹⁴⁷ [i]