MinT - Best Known (88, 88+59, s)-Nets in Base 3

Best Known (88, 88+59, s)-Nets in Base 3

(88, 88+59, 128)-Net over F₃ — Constructive and digital

Digital (88, 147, 128)-net over F₃, using

3 times m-reduction [i] based on digital (88, 150, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 75, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(88, 88+59, 143)-Net over F₃ — Digital

Digital (88, 147, 143)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+59, 1444)-Net in Base 3 — Upper bound on s

There is no (88, 147, 1445)-net in base 3, because

1 times m-reduction [i] would yield (88, 146, 1445)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4608 255046 433510 115897 542034 541836 042685 661534 520271 927025 578509 930747 > 3¹⁴⁶ [i]