MinT - Best Known (247−107, 247, s)-Nets in Base 3

Best Known (247−107, 247, s)-Nets in Base 3

(247−107, 247, 128)-Net over F₃ — Constructive and digital

Digital (140, 247, 128)-net over F₃, using

t-expansion [i] based on digital (138, 247, 128)-net over F₃, using
- 3 times m-reduction [i] based on digital (138, 250, 128)-net over F₃, using
  - trace code for nets [i] based on digital (13, 125, 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]

(247−107, 247, 180)-Net over F₃ — Digital

Digital (140, 247, 180)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−107, 247, 1635)-Net in Base 3 — Upper bound on s

There is no (140, 247, 1636)-net in base 3, because

1 times m-reduction [i] would yield (140, 246, 1636)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2355 543306 273136 531463 992666 204353 866164 280859 117998 758247 270319 823993 471649 573893 210416 513677 145533 343731 975493 238953 > 3²⁴⁶ [i]