MinT - Best Known (178−47, 178, s)-Nets in Base 3

Best Known (178−47, 178, s)-Nets in Base 3

(178−47, 178, 288)-Net over F₃ — Constructive and digital

Digital (131, 178, 288)-net over F₃, using

2 times m-reduction [i] based on digital (131, 180, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 60, 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]

(178−47, 178, 626)-Net over F₃ — Digital

Digital (131, 178, 626)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−47, 178, 22117)-Net in Base 3 — Upper bound on s

There is no (131, 178, 22118)-net in base 3, because

1 times m-reduction [i] would yield (131, 177, 22118)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 821642 053816 490656 878653 985352 458044 494680 682087 340231 771858 018215 195316 762380 701433 > 3¹⁷⁷ [i]