MinT - Best Known (126−39, 126, s)-Nets in Base 9

Best Known (126−39, 126, s)-Nets in Base 9

(126−39, 126, 740)-Net over F₉ — Constructive and digital

Digital (87, 126, 740)-net over F₉, using

16 times m-reduction [i] based on digital (87, 142, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 71, 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]

(126−39, 126, 2759)-Net over F₉ — Digital

Digital (87, 126, 2759)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−39, 126, 1879464)-Net in Base 9 — Upper bound on s

There is no (87, 126, 1879465)-net in base 9, because

1 times m-reduction [i] would yield (87, 125, 1879465)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 190684 626580 600587 049161 117865 886536 319220 846996 664449 442657 798071 099548 699410 098967 049660 683757 771123 814546 709890 076185 > 9¹²⁵ [i]