MinT - Best Known (163−65, 163, s)-Nets in Base 3

Best Known (163−65, 163, s)-Nets in Base 3

(163−65, 163, 128)-Net over F₃ — Constructive and digital

Digital (98, 163, 128)-net over F₃, using

7 times m-reduction [i] based on digital (98, 170, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 85, 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]

(163−65, 163, 158)-Net over F₃ — Digital

Digital (98, 163, 158)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−65, 163, 1633)-Net in Base 3 — Upper bound on s

There is no (98, 163, 1634)-net in base 3, because

1 times m-reduction [i] would yield (98, 162, 1634)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 199600 082835 353115 109808 145701 770303 474241 552690 560473 584649 724072 953883 828545 > 3¹⁶² [i]