MinT - Best Known (234−115, 234, s)-Nets in Base 3

Best Known (234−115, 234, s)-Nets in Base 3

(234−115, 234, 76)-Net over F₃ — Constructive and digital

Digital (119, 234, 76)-net over F₃, using

net from sequence [i] based on digital (119, 75)-sequence over F₃, using
- base reduction for sequences [i] based on digital (22, 75)-sequence over F₉, using
  - s-reduction based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(234−115, 234, 121)-Net over F₃ — Digital

Digital (119, 234, 121)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−115, 234, 929)-Net in Base 3 — Upper bound on s

There is no (119, 234, 930)-net in base 3, because

1 times m-reduction [i] would yield (119, 233, 930)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1519 206307 267127 437804 656609 640225 553948 904171 349346 720502 776996 903991 451874 757584 538842 468320 839861 155600 231061 > 3²³³ [i]