MinT - Best Known (245−48, 245, s)-Nets in Base 3

Best Known (245−48, 245, s)-Nets in Base 3

(245−48, 245, 896)-Net over F₃ — Constructive and digital

Digital (197, 245, 896)-net over F₃, using

3¹ times duplication [i] based on digital (196, 244, 896)-net over F₃, using
- trace code for nets [i] based on digital (13, 61, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(245−48, 245, 2843)-Net over F₃ — Digital

Digital (197, 245, 2843)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−48, 245, 363845)-Net in Base 3 — Upper bound on s

There is no (197, 245, 363846)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 784 711294 644331 521545 326296 473634 788973 693294 868475 427257 898587 917852 600216 401284 750158 389025 657580 906144 096399 024241 > 3²⁴⁵ [i]