MinT - Best Known (148−42, 148, s)-Nets in Base 3

Best Known (148−42, 148, s)-Nets in Base 3

(148−42, 148, 246)-Net over F₃ — Constructive and digital

Digital (106, 148, 246)-net over F₃, using

3¹ times duplication [i] based on digital (105, 147, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 49, 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]

(148−42, 148, 415)-Net over F₃ — Digital

Digital (106, 148, 415)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−42, 148, 9980)-Net in Base 3 — Upper bound on s

There is no (106, 148, 9981)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41175 407785 876728 910935 950130 759391 224155 769942 489907 310977 307837 218251 > 3¹⁴⁸ [i]