MinT - Best Known (63, 63+24, s)-Nets in Base 3

Best Known (63, 63+24, s)-Nets in Base 3

(63, 63+24, 204)-Net over F₃ — Constructive and digital

Digital (63, 87, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 29, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(63, 63+24, 312)-Net over F₃ — Digital

Digital (63, 87, 312)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+24, 7599)-Net in Base 3 — Upper bound on s

There is no (63, 87, 7600)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 323341 180527 852442 567620 301584 349810 273921 > 3⁸⁷ [i]