MinT - Best Known (150, 150+64, s)-Nets in Base 3

Best Known (150, 150+64, s)-Nets in Base 3

(150, 150+64, 246)-Net over F₃ — Constructive and digital

Digital (150, 214, 246)-net over F₃, using

3¹ times duplication [i] based on digital (149, 213, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 71, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(150, 150+64, 475)-Net over F₃ — Digital

Digital (150, 214, 475)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+64, 9890)-Net in Base 3 — Upper bound on s

There is no (150, 214, 9891)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 272345 728151 683205 912605 171323 749606 622371 688779 379849 054625 004972 629473 589002 403836 289167 164431 709633 > 3²¹⁴ [i]