MinT - Best Known (149, 149+68, s)-Nets in Base 3

Best Known (149, 149+68, s)-Nets in Base 3

(149, 149+68, 192)-Net over F₃ — Constructive and digital

Digital (149, 217, 192)-net over F₃, using

3¹ times duplication [i] based on digital (148, 216, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 72, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(149, 149+68, 415)-Net over F₃ — Digital

Digital (149, 217, 415)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+68, 7475)-Net in Base 3 — Upper bound on s

There is no (149, 217, 7476)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 316858 371739 312229 771255 786487 486388 865604 026335 640197 116555 539032 361067 096492 431987 711292 725377 634393 > 3²¹⁷ [i]