MinT - Best Known (63, 63+41, s)-Nets in Base 9

Best Known (63, 63+41, s)-Nets in Base 9

(63, 63+41, 344)-Net over F₉ — Constructive and digital

Digital (63, 104, 344)-net over F₉, using

8 times m-reduction [i] based on digital (63, 112, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 56, 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]

(63, 63+41, 617)-Net over F₉ — Digital

Digital (63, 104, 617)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+41, 85212)-Net in Base 9 — Upper bound on s

There is no (63, 104, 85213)-net in base 9, because

1 times m-reduction [i] would yield (63, 103, 85213)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 193 649004 686605 970234 635594 395544 682332 548287 461120 138710 407774 490626 515935 606457 762243 255975 659681 > 9¹⁰³ [i]