MinT - Best Known (145, 145+48, s)-Nets in Base 3

Best Known (145, 145+48, s)-Nets in Base 3

(145, 145+48, 328)-Net over F₃ — Constructive and digital

Digital (145, 193, 328)-net over F₃, using

3¹ times duplication [i] based on digital (144, 192, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 48, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(145, 145+48, 843)-Net over F₃ — Digital

Digital (145, 193, 843)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+48, 33641)-Net in Base 3 — Upper bound on s

There is no (145, 193, 33642)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 121 465728 274394 571483 030084 054667 724716 907162 796979 723080 822167 668872 661865 915458 103731 839601 > 3¹⁹³ [i]