MinT - Best Known (149, 149+65, s)-Nets in Base 3

Best Known (149, 149+65, s)-Nets in Base 3

(149, 149+65, 228)-Net over F₃ — Constructive and digital

Digital (149, 214, 228)-net over F₃, using

3¹ times duplication [i] based on digital (148, 213, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 71, 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]

(149, 149+65, 452)-Net over F₃ — Digital

Digital (149, 214, 452)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+65, 9555)-Net in Base 3 — Upper bound on s

There is no (149, 214, 9556)-net in base 3, because

1 times m-reduction [i] would yield (149, 213, 9556)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423933 372547 128348 970290 856169 023803 859098 137029 931707 220488 963774 900899 360632 492880 477343 754460 249345 > 3²¹³ [i]