MinT - Best Known (98−55, 98, s)-Nets in Base 9

Best Known (98−55, 98, s)-Nets in Base 9

(98−55, 98, 92)-Net over F₉ — Constructive and digital

Digital (43, 98, 92)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 30, 28)-net over F₉, using
  - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]
2. digital (13, 68, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(98−55, 98, 94)-Net in Base 9 — Constructive

(43, 98, 94)-net in base 9, using

1 times m-reduction [i] based on (43, 99, 94)-net in base 9, using
- base change [i] based on digital (10, 66, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(98−55, 98, 147)-Net over F₉ — Digital

Digital (43, 98, 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]

(98−55, 98, 3643)-Net in Base 9 — Upper bound on s

There is no (43, 98, 3644)-net in base 9, because

1 times m-reduction [i] would yield (43, 97, 3644)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 364 391223 077734 480534 706253 675316 298806 096356 472506 884292 851093 973072 552759 568381 524570 833185 > 9⁹⁷ [i]