MinT - Best Known (172, 172+71, s)-Nets in Base 3

Best Known (172, 172+71, s)-Nets in Base 3

(172, 172+71, 282)-Net over F₃ — Constructive and digital

Digital (172, 243, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 81, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(172, 172+71, 572)-Net over F₃ — Digital

Digital (172, 243, 572)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+71, 13807)-Net in Base 3 — Upper bound on s

There is no (172, 243, 13808)-net in base 3, because

1 times m-reduction [i] would yield (172, 242, 13808)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 126375 001352 572698 119130 845298 730630 079028 292150 498283 875049 135492 021356 877620 828902 707648 961648 178131 753317 186497 > 3²⁴² [i]