MinT - Best Known (148, 148+60, s)-Nets in Base 3

Best Known (148, 148+60, s)-Nets in Base 3

(148, 148+60, 264)-Net over F₃ — Constructive and digital

Digital (148, 208, 264)-net over F₃, using

3¹ times duplication [i] based on digital (147, 207, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 69, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(148, 148+60, 521)-Net over F₃ — Digital

Digital (148, 208, 521)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+60, 12211)-Net in Base 3 — Upper bound on s

There is no (148, 208, 12212)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1746 816652 267122 197595 711217 626177 983273 762631 723274 017600 110396 311411 977850 288464 338486 609482 158073 > 3²⁰⁸ [i]