MinT - Best Known (142−39, 142, s)-Nets in Base 3

Best Known (142−39, 142, s)-Nets in Base 3

(142−39, 142, 252)-Net over F₃ — Constructive and digital

Digital (103, 142, 252)-net over F₃, using

3¹ times duplication [i] based on digital (102, 141, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 47, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(142−39, 142, 452)-Net over F₃ — Digital

Digital (103, 142, 452)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−39, 142, 13751)-Net in Base 3 — Upper bound on s

There is no (103, 142, 13752)-net in base 3, because

1 times m-reduction [i] would yield (103, 141, 13752)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 815404 055127 452820 451066 110679 385720 290732 802501 462712 279772 286049 > 3¹⁴¹ [i]