MinT - Best Known (198−53, 198, s)-Nets in Base 3

Best Known (198−53, 198, s)-Nets in Base 3

(198−53, 198, 288)-Net over F₃ — Constructive and digital

Digital (145, 198, 288)-net over F₃, using

3 times m-reduction [i] based on digital (145, 201, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 67, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(198−53, 198, 649)-Net over F₃ — Digital

Digital (145, 198, 649)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−53, 198, 21720)-Net in Base 3 — Upper bound on s

There is no (145, 198, 21721)-net in base 3, because

1 times m-reduction [i] would yield (145, 197, 21721)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9846 411285 761535 900073 362401 498638 767881 718165 004261 157568 887970 838475 187047 364092 368445 141337 > 3¹⁹⁷ [i]