MinT - Best Known (116, 116+87, s)-Nets in Base 3

Best Known (116, 116+87, s)-Nets in Base 3

(116, 116+87, 128)-Net over F₃ — Constructive and digital

Digital (116, 203, 128)-net over F₃, using

3 times m-reduction [i] based on digital (116, 206, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 103, 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]

(116, 116+87, 156)-Net over F₃ — Digital

Digital (116, 203, 156)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+87, 1429)-Net in Base 3 — Upper bound on s

There is no (116, 203, 1430)-net in base 3, because

1 times m-reduction [i] would yield (116, 202, 1430)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 416167 607910 214782 507334 056152 525242 715102 590470 422220 392223 808272 192489 972920 141493 047604 339089 > 3²⁰² [i]