MinT - Best Known (148−45, 148, s)-Nets in Base 3

Best Known (148−45, 148, s)-Nets in Base 3

(148−45, 148, 192)-Net over F₃ — Constructive and digital

Digital (103, 148, 192)-net over F₃, using

3¹ times duplication [i] based on digital (102, 147, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 49, 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]

(148−45, 148, 329)-Net over F₃ — Digital

Digital (103, 148, 329)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−45, 148, 6958)-Net in Base 3 — Upper bound on s

There is no (103, 148, 6959)-net in base 3, because

1 times m-reduction [i] would yield (103, 147, 6959)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13720 159212 032886 808823 062107 606213 802566 337239 310947 635436 795347 875509 > 3¹⁴⁷ [i]