MinT - Best Known (82, 128, s)-Nets in Base 9

Best Known (82, 128, s)-Nets in Base 9

(82, 128, 740)-Net over F₉ — Constructive and digital

Digital (82, 128, 740)-net over F₉, using

4 times m-reduction [i] based on digital (82, 132, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 66, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(82, 128, 1164)-Net over F₉ — Digital

Digital (82, 128, 1164)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 128, 240939)-Net in Base 9 — Upper bound on s

There is no (82, 128, 240940)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 139 012965 171597 208923 755809 925664 835324 280310 699237 711595 028633 377693 790055 883169 077571 935147 259074 164638 788937 588127 721761 > 9¹²⁸ [i]