MinT - Best Known (178−45, 178, s)-Nets in Base 3

Best Known (178−45, 178, s)-Nets in Base 3

(178−45, 178, 288)-Net over F₃ — Constructive and digital

Digital (133, 178, 288)-net over F₃, using

5 times m-reduction [i] based on digital (133, 183, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 61, 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]

(178−45, 178, 740)-Net over F₃ — Digital

Digital (133, 178, 740)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−45, 178, 31201)-Net in Base 3 — Upper bound on s

There is no (133, 178, 31202)-net in base 3, because

1 times m-reduction [i] would yield (133, 177, 31202)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 821540 312399 700192 195725 855931 486616 592711 597045 322406 561179 133263 536242 684818 378781 > 3¹⁷⁷ [i]