MinT - Best Known (119, 119+113, s)-Nets in Base 3

Best Known (119, 119+113, s)-Nets in Base 3

(119, 119+113, 76)-Net over F₃ — Constructive and digital

Digital (119, 232, 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]

(119, 119+113, 123)-Net over F₃ — Digital

Digital (119, 232, 123)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+113, 954)-Net in Base 3 — Upper bound on s

There is no (119, 232, 955)-net in base 3, because

1 times m-reduction [i] would yield (119, 231, 955)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 169 863614 899786 737137 064657 742028 448358 772724 203436 273275 621307 254944 549245 876817 764029 678652 031549 834528 401681 > 3²³¹ [i]