MinT - Best Known (229−101, 229, s)-Nets in Base 3

Best Known (229−101, 229, s)-Nets in Base 3

(229−101, 229, 128)-Net over F₃ — Constructive and digital

Digital (128, 229, 128)-net over F₃, using

1 times m-reduction [i] based on digital (128, 230, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 115, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(229−101, 229, 160)-Net over F₃ — Digital

Digital (128, 229, 160)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−101, 229, 1411)-Net in Base 3 — Upper bound on s

There is no (128, 229, 1412)-net in base 3, because

1 times m-reduction [i] would yield (128, 228, 1412)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 282868 428517 014751 618252 518734 674709 443972 416678 664798 942711 707048 867559 852033 072497 990993 796007 276379 688761 > 3²²⁸ [i]