MinT - Best Known (178−48, 178, s)-Nets in Base 3

Best Known (178−48, 178, s)-Nets in Base 3

(178−48, 178, 288)-Net over F₃ — Constructive and digital

Digital (130, 178, 288)-net over F₃, using

3¹ times duplication [i] based on digital (129, 177, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 59, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(178−48, 178, 579)-Net over F₃ — Digital

Digital (130, 178, 579)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−48, 178, 16919)-Net in Base 3 — Upper bound on s

There is no (130, 178, 16920)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 473852 392179 637264 551206 403565 975981 423663 135434 692161 844608 022024 300417 035033 281793 > 3¹⁷⁸ [i]