MinT - Best Known (123−93, 123, s)-Nets in Base 9

Best Known (123−93, 123, s)-Nets in Base 9

(123−93, 123, 78)-Net over F₉ — Constructive and digital

Digital (30, 123, 78)-net over F₉, using

t-expansion [i] based on digital (22, 123, 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]

(123−93, 123, 110)-Net over F₉ — Digital

Digital (30, 123, 110)-net over F₉, using

t-expansion [i] based on digital (26, 123, 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]

(123−93, 123, 735)-Net in Base 9 — Upper bound on s

There is no (30, 123, 736)-net in base 9, because

1 times m-reduction [i] would yield (30, 122, 736)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 264 556777 536523 379363 954904 518542 368076 869077 193661 970621 665196 147054 662565 358089 828750 449002 399611 644129 113390 192129 > 9¹²² [i]