MinT - Best Known (148−44, 148, s)-Nets in Base 3

Best Known (148−44, 148, s)-Nets in Base 3

(148−44, 148, 204)-Net over F₃ — Constructive and digital

Digital (104, 148, 204)-net over F₃, using

3¹ times duplication [i] based on digital (103, 147, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 49, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(148−44, 148, 354)-Net over F₃ — Digital

Digital (104, 148, 354)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−44, 148, 7316)-Net in Base 3 — Upper bound on s

There is no (104, 148, 7317)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41230 597489 439587 467983 331318 127009 612679 307715 916418 218972 946535 517473 > 3¹⁴⁸ [i]