MinT - Best Known (148−67, 148, s)-Nets in Base 3

Best Known (148−67, 148, s)-Nets in Base 3

(148−67, 148, 72)-Net over F₃ — Constructive and digital

Digital (81, 148, 72)-net over F₃, using

trace code for nets [i] based on digital (7, 74, 36)-net over F₉, using
- net from sequence [i] based on digital (7, 35)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
    - a function field by SÃ©mirat [i]

(148−67, 148, 102)-Net over F₃ — Digital

Digital (81, 148, 102)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−67, 148, 846)-Net in Base 3 — Upper bound on s

There is no (81, 148, 847)-net in base 3, because

1 times m-reduction [i] would yield (81, 147, 847)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 14030 393197 016216 749797 732637 925388 445848 604678 483343 187778 259743 389279 > 3¹⁴⁷ [i]