MinT - Best Known (198−83, 198, s)-Nets in Base 3

Best Known (198−83, 198, s)-Nets in Base 3

(198−83, 198, 128)-Net over F₃ — Constructive and digital

Digital (115, 198, 128)-net over F₃, using

6 times m-reduction [i] based on digital (115, 204, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 102, 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]

(198−83, 198, 162)-Net over F₃ — Digital

Digital (115, 198, 162)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−83, 198, 1542)-Net in Base 3 — Upper bound on s

There is no (115, 198, 1543)-net in base 3, because

1 times m-reduction [i] would yield (115, 197, 1543)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9939 061520 373554 208914 954499 765681 533766 312236 287648 300404 197096 158272 894700 039330 306581 678015 > 3¹⁹⁷ [i]