MinT - Best Known (98, 165, s)-Nets in Base 3

Best Known (98, 165, s)-Nets in Base 3

(98, 165, 128)-Net over F₃ — Constructive and digital

Digital (98, 165, 128)-net over F₃, using

5 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]

(98, 165, 152)-Net over F₃ — Digital

Digital (98, 165, 152)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 165, 1514)-Net in Base 3 — Upper bound on s

There is no (98, 165, 1515)-net in base 3, because

1 times m-reduction [i] would yield (98, 164, 1515)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 780348 275092 345476 919550 298597 327096 319594 319217 896872 539139 739301 042195 881111 > 3¹⁶⁴ [i]