MinT - Best Known (98, 98+39, s)-Nets in Base 3

Best Known (98, 98+39, s)-Nets in Base 3

(98, 98+39, 228)-Net over F₃ — Constructive and digital

Digital (98, 137, 228)-net over F₃, using

1 times m-reduction [i] based on digital (98, 138, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 46, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(98, 98+39, 386)-Net over F₃ — Digital

Digital (98, 137, 386)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+39, 10294)-Net in Base 3 — Upper bound on s

There is no (98, 137, 10295)-net in base 3, because

1 times m-reduction [i] would yield (98, 136, 10295)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 77478 210271 840303 923400 659443 197215 228052 191772 849419 917143 451835 > 3¹³⁶ [i]