MinT - Best Known (236−63, 236, s)-Nets in Base 3

Best Known (236−63, 236, s)-Nets in Base 3

(236−63, 236, 288)-Net over F₃ — Constructive and digital

Digital (173, 236, 288)-net over F₃, using

7 times m-reduction [i] based on digital (173, 243, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 81, 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]

(236−63, 236, 761)-Net over F₃ — Digital

Digital (173, 236, 761)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−63, 236, 25666)-Net in Base 3 — Upper bound on s

There is no (173, 236, 25667)-net in base 3, because

1 times m-reduction [i] would yield (173, 235, 25667)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13289 764746 372581 462931 396759 129785 327737 788125 354313 638984 891192 121103 090613 024814 566940 082883 063339 455578 840275 > 3²³⁵ [i]