MinT - Best Known (99−47, 99, s)-Nets in Base 9

Best Known (99−47, 99, s)-Nets in Base 9

(99−47, 99, 232)-Net over F₉ — Constructive and digital

Digital (52, 99, 232)-net over F₉, using

1 times m-reduction [i] based on digital (52, 100, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 50, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(99−47, 99, 244)-Net over F₉ — Digital

Digital (52, 99, 244)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−47, 99, 13703)-Net in Base 9 — Upper bound on s

There is no (52, 99, 13704)-net in base 9, because

1 times m-reduction [i] would yield (52, 98, 13704)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3282 234181 966894 509017 556600 650165 866193 285229 176074 029425 115563 388210 076426 103673 328072 523457 > 9⁹⁸ [i]