MinT - Best Known (180−74, 180, s)-Nets in Base 3

Best Known (180−74, 180, s)-Nets in Base 3

(180−74, 180, 128)-Net over F₃ — Constructive and digital

Digital (106, 180, 128)-net over F₃, using

6 times m-reduction [i] based on digital (106, 186, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 93, 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]

(180−74, 180, 158)-Net over F₃ — Digital

Digital (106, 180, 158)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−74, 180, 1498)-Net in Base 3 — Upper bound on s

There is no (106, 180, 1499)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 77 067783 337045 663084 666174 491169 089117 739339 061616 461536 910509 683790 596185 294981 464367 > 3¹⁸⁰ [i]