MinT - Best Known (182−77, 182, s)-Nets in Base 3

Best Known (182−77, 182, s)-Nets in Base 3

(182−77, 182, 128)-Net over F₃ — Constructive and digital

Digital (105, 182, 128)-net over F₃, using

2 times m-reduction [i] based on digital (105, 184, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 92, 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]

(182−77, 182, 147)-Net over F₃ — Digital

Digital (105, 182, 147)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−77, 182, 1370)-Net in Base 3 — Upper bound on s

There is no (105, 182, 1371)-net in base 3, because

1 times m-reduction [i] would yield (105, 181, 1371)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 233 649192 628550 135979 089296 558531 906288 454900 448348 290004 420570 138080 434560 091387 827277 > 3¹⁸¹ [i]