MinT - Best Known (118, 118+97, s)-Nets in Base 3

Best Known (118, 118+97, s)-Nets in Base 3

(118, 118+97, 80)-Net over F₃ — Constructive and digital

Digital (118, 215, 80)-net over F₃, using

5 times m-reduction [i] based on digital (118, 220, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 110, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(118, 118+97, 142)-Net over F₃ — Digital

Digital (118, 215, 142)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+97, 1209)-Net in Base 3 — Upper bound on s

There is no (118, 215, 1210)-net in base 3, because

1 times m-reduction [i] would yield (118, 214, 1210)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 317494 207603 015195 534806 844670 513104 443814 311015 159585 032211 348027 885317 756715 087011 302687 675844 528353 > 3²¹⁴ [i]