MinT - Best Known (89, 89+42, s)-Nets in Base 9

Best Known (89, 89+42, s)-Nets in Base 9

(89, 89+42, 740)-Net over F₉ — Constructive and digital

Digital (89, 131, 740)-net over F₉, using

15 times m-reduction [i] based on digital (89, 146, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 73, 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]

(89, 89+42, 2279)-Net over F₉ — Digital

Digital (89, 131, 2279)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+42, 972865)-Net in Base 9 — Upper bound on s

There is no (89, 131, 972866)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101339 255582 848767 596316 195409 228974 847580 892116 681999 410497 601235 089907 936070 197112 543416 659782 553168 825588 315044 064117 799121 > 9¹³¹ [i]