MinT - Best Known (229−55, 229, s)-Nets in Base 3

Best Known (229−55, 229, s)-Nets in Base 3

(229−55, 229, 464)-Net over F₃ — Constructive and digital

Digital (174, 229, 464)-net over F₃, using

3¹ times duplication [i] based on digital (173, 228, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 57, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(229−55, 229, 1116)-Net over F₃ — Digital

Digital (174, 229, 1116)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−55, 229, 58371)-Net in Base 3 — Upper bound on s

There is no (174, 229, 58372)-net in base 3, because

1 times m-reduction [i] would yield (174, 228, 58372)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 076755 611565 450359 829232 798854 783236 814795 863374 015741 110691 321364 060662 840426 761740 251551 936487 935887 563121 > 3²²⁸ [i]