MinT - Best Known (147−71, 147, s)-Nets in Base 9

Best Known (147−71, 147, s)-Nets in Base 9

(147−71, 147, 232)-Net over F₉ — Constructive and digital

Digital (76, 147, 232)-net over F₉, using

1 times m-reduction [i] based on digital (76, 148, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 74, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(147−71, 147, 316)-Net over F₉ — Digital

Digital (76, 147, 316)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−71, 147, 16602)-Net in Base 9 — Upper bound on s

There is no (76, 147, 16603)-net in base 9, because

1 times m-reduction [i] would yield (76, 146, 16603)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 892765 583198 158061 974908 362622 352071 945152 892169 821276 458034 369607 813133 969590 894543 863546 246373 507959 677762 544831 419167 230870 862580 553481 > 9¹⁴⁶ [i]