MinT - Best Known (64, 64+43, s)-Nets in Base 9

Best Known (64, 64+43, s)-Nets in Base 9

(64, 64+43, 344)-Net over F₉ — Constructive and digital

Digital (64, 107, 344)-net over F₉, using

7 times m-reduction [i] based on digital (64, 114, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 57, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(64, 64+43, 570)-Net over F₉ — Digital

Digital (64, 107, 570)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+43, 71117)-Net in Base 9 — Upper bound on s

There is no (64, 107, 71118)-net in base 9, because

1 times m-reduction [i] would yield (64, 106, 71118)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 141167 540361 358140 026897 442694 775048 489583 658431 967027 690619 456634 587113 366891 975052 382736 225598 080945 > 9¹⁰⁶ [i]