MinT - Best Known (216−53, 216, s)-Nets in Base 3

Best Known (216−53, 216, s)-Nets in Base 3

(216−53, 216, 400)-Net over F₃ — Constructive and digital

Digital (163, 216, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 54, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(216−53, 216, 975)-Net over F₃ — Digital

Digital (163, 216, 975)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−53, 216, 46499)-Net in Base 3 — Upper bound on s

There is no (163, 216, 46500)-net in base 3, because

1 times m-reduction [i] would yield (163, 215, 46500)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 811770 277631 625582 499473 761652 388990 969396 601363 382731 238844 230543 161549 963754 719431 124135 941097 638521 > 3²¹⁵ [i]