MinT - Best Known (137−67, 137, s)-Nets in Base 9

Best Known (137−67, 137, s)-Nets in Base 9

(137−67, 137, 200)-Net over F₉ — Constructive and digital

Digital (70, 137, 200)-net over F₉, using

1 times m-reduction [i] based on digital (70, 138, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 69, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(137−67, 137, 282)-Net over F₉ — Digital

Digital (70, 137, 282)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−67, 137, 14069)-Net in Base 9 — Upper bound on s

There is no (70, 137, 14070)-net in base 9, because

1 times m-reduction [i] would yield (70, 136, 14070)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 5990 528967 754644 959605 724143 301913 744441 116541 097936 138842 073030 096497 226591 022030 451215 419441 636806 347174 834066 150927 339797 471665 > 9¹³⁶ [i]