MinT - Best Known (148−55, 148, s)-Nets in Base 9

Best Known (148−55, 148, s)-Nets in Base 9

(148−55, 148, 740)-Net over F₉ — Constructive and digital

Digital (93, 148, 740)-net over F₉, using

t-expansion [i] based on digital (91, 148, 740)-net over F₉, using
- 2 times m-reduction [i] based on digital (91, 150, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 75, 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]

(148−55, 148, 1108)-Net over F₉ — Digital

Digital (93, 148, 1108)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−55, 148, 214093)-Net in Base 9 — Upper bound on s

There is no (93, 148, 214094)-net in base 9, because

1 times m-reduction [i] would yield (93, 147, 214094)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 187 786801 371728 990652 459770 095889 035972 385724 498572 446252 934507 709518 330004 697550 665607 001486 224160 216266 049950 371034 078009 339666 805810 272145 > 9¹⁴⁷ [i]