MinT - Best Known (88, 88+73, s)-Nets in Base 3

Best Known (88, 88+73, s)-Nets in Base 3

(88, 88+73, 72)-Net over F₃ — Constructive and digital

Digital (88, 161, 72)-net over F₃, using

1 times m-reduction [i] based on digital (88, 162, 72)-net over F₃, using
- trace code for nets [i] based on digital (7, 81, 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]

(88, 88+73, 109)-Net over F₃ — Digital

Digital (88, 161, 109)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+73, 907)-Net in Base 3 — Upper bound on s

There is no (88, 161, 908)-net in base 3, because

1 times m-reduction [i] would yield (88, 160, 908)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22294 181470 557201 238462 383044 561979 130650 070444 642624 249231 418704 130047 462785 > 3¹⁶⁰ [i]