MinT - Best Known (147−51, 147, s)-Nets in Base 9

Best Known (147−51, 147, s)-Nets in Base 9

(147−51, 147, 740)-Net over F₉ — Constructive and digital

Digital (96, 147, 740)-net over F₉, using

t-expansion [i] based on digital (91, 147, 740)-net over F₉, using
- 3 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]

(147−51, 147, 1581)-Net over F₉ — Digital

Digital (96, 147, 1581)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−51, 147, 475661)-Net in Base 9 — Upper bound on s

There is no (96, 147, 475662)-net in base 9, because

1 times m-reduction [i] would yield (96, 146, 475662)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 864629 026155 913076 615612 583419 223719 776025 244686 793471 543098 374843 508507 898568 675044 143124 786516 056679 767795 135049 288013 185053 362504 556017 > 9¹⁴⁶ [i]