MinT - Best Known (138−54, 138, s)-Nets in Base 9

Best Known (138−54, 138, s)-Nets in Base 9

(138−54, 138, 448)-Net over F₉ — Constructive and digital

Digital (84, 138, 448)-net over F₉, using

4 times m-reduction [i] based on digital (84, 142, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 71, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(138−54, 138, 798)-Net over F₉ — Digital

Digital (84, 138, 798)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−54, 138, 102917)-Net in Base 9 — Upper bound on s

There is no (84, 138, 102918)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 484817 659919 975063 896245 384593 177781 798197 373972 497972 547318 459887 612427 850887 742933 791957 882669 397536 266354 036273 282810 985587 611601 > 9¹³⁸ [i]