MinT - Best Known (114, 114+89, s)-Nets in Base 3

Best Known (114, 114+89, s)-Nets in Base 3

(114, 114+89, 80)-Net over F₃ — Constructive and digital

Digital (114, 203, 80)-net over F₃, using

9 times m-reduction [i] based on digital (114, 212, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 106, 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]

(114, 114+89, 146)-Net over F₃ — Digital

Digital (114, 203, 146)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+89, 1294)-Net in Base 3 — Upper bound on s

There is no (114, 203, 1295)-net in base 3, because

1 times m-reduction [i] would yield (114, 202, 1295)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 419076 609106 599346 265394 762046 593634 716176 760826 807871 763303 730439 651220 163277 860068 707918 885545 > 3²⁰² [i]