MinT - Best Known (88, 88+65, s)-Nets in Base 3

Best Known (88, 88+65, s)-Nets in Base 3

(88, 88+65, 80)-Net over F₃ — Constructive and digital

Digital (88, 153, 80)-net over F₃, using

7 times m-reduction [i] based on digital (88, 160, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 80, 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]

(88, 88+65, 125)-Net over F₃ — Digital

Digital (88, 153, 125)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+65, 1149)-Net in Base 3 — Upper bound on s

There is no (88, 153, 1150)-net in base 3, because

1 times m-reduction [i] would yield (88, 152, 1150)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 362008 859172 107781 609078 229075 197938 178017 929568 456336 286763 333047 117633 > 3¹⁵² [i]