MinT - Best Known (119, 249, s)-Nets in Base 3

Best Known (119, 249, s)-Nets in Base 3

(119, 249, 76)-Net over F₃ — Constructive and digital

Digital (119, 249, 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, 249, 120)-Net over F₃ — Digital

Digital (119, 249, 120)-net over F₃, using

t-expansion [i] based on digital (113, 249, 120)-net over F₃, using
- net from sequence [i] based on digital (113, 119)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(119, 249, 779)-Net in Base 3 — Upper bound on s

There is no (119, 249, 780)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65089 745846 498702 528161 401610 516637 758968 682663 336104 085294 999822 412381 715111 920657 901390 296143 074617 099562 210357 274137 > 3²⁴⁹ [i]