MinT - Best Known (63, 63+25, s)-Nets in Base 3

Best Known (63, 63+25, s)-Nets in Base 3

(63, 63+25, 192)-Net over F₃ — Constructive and digital

Digital (63, 88, 192)-net over F₃, using

3¹ times duplication [i] based on digital (62, 87, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 29, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(63, 63+25, 282)-Net over F₃ — Digital

Digital (63, 88, 282)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+25, 7599)-Net in Base 3 — Upper bound on s

There is no (63, 88, 7600)-net in base 3, because

1 times m-reduction [i] would yield (63, 87, 7600)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 323341 180527 852442 567620 301584 349810 273921 > 3⁸⁷ [i]