MinT - Best Known (119, 220, s)-Nets in Base 3

Best Known (119, 220, s)-Nets in Base 3

(119, 220, 80)-Net over F₃ — Constructive and digital

Digital (119, 220, 80)-net over F₃, using

2 times m-reduction [i] based on digital (119, 222, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 111, 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]

(119, 220, 138)-Net over F₃ — Digital

Digital (119, 220, 138)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 220, 1149)-Net in Base 3 — Upper bound on s

There is no (119, 220, 1150)-net in base 3, because

1 times m-reduction [i] would yield (119, 219, 1150)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 318 669122 104721 063516 783162 128876 020636 284253 904576 696318 127968 397888 397942 080453 349779 384136 139861 821789 > 3²¹⁹ [i]