MinT - Best Known (132, 132+58, s)-Nets in Base 3

Best Known (132, 132+58, s)-Nets in Base 3

(132, 132+58, 204)-Net over F₃ — Constructive and digital

Digital (132, 190, 204)-net over F₃, using

3¹ times duplication [i] based on digital (131, 189, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 63, 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]

(132, 132+58, 401)-Net over F₃ — Digital

Digital (132, 190, 401)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+58, 7770)-Net in Base 3 — Upper bound on s

There is no (132, 190, 7771)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 499839 452631 320119 266792 723685 508922 991209 731259 819706 263433 024056 877249 668372 981901 883903 > 3¹⁹⁰ [i]