MinT - Best Known (57, 57+23, s)-Nets in Base 9

Best Known (57, 57+23, s)-Nets in Base 9

(57, 57+23, 740)-Net over F₉ — Constructive and digital

Digital (57, 80, 740)-net over F₉, using

2 times m-reduction [i] based on digital (57, 82, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 41, 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]

(57, 57+23, 3351)-Net over F₉ — Digital

Digital (57, 80, 3351)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+23, 4376427)-Net in Base 9 — Upper bound on s

There is no (57, 80, 4376428)-net in base 9, because

1 times m-reduction [i] would yield (57, 79, 4376428)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2427 497353 726716 107293 991930 682067 316284 036474 127459 540798 802110 510960 437665 > 9⁷⁹ [i]