MinT - Best Known (29, 29+34, s)-Nets in Base 9

Best Known (29, 29+34, s)-Nets in Base 9

(29, 29+34, 78)-Net over F₉ — Constructive and digital

Digital (29, 63, 78)-net over F₉, using

t-expansion [i] based on digital (22, 63, 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]

(29, 29+34, 84)-Net in Base 9 — Constructive

(29, 63, 84)-net in base 9, using

base change [i] based on digital (8, 42, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(29, 29+34, 110)-Net over F₉ — Digital

Digital (29, 63, 110)-net over F₉, using

t-expansion [i] based on digital (26, 63, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(29, 29+34, 3074)-Net in Base 9 — Upper bound on s

There is no (29, 63, 3075)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 315449 426090 836714 603487 058910 745610 030040 346664 669237 579161 > 9⁶³ [i]