MinT - Best Known (247−74, 247, s)-Nets in Base 3

Best Known (247−74, 247, s)-Nets in Base 3

(247−74, 247, 252)-Net over F₃ — Constructive and digital

Digital (173, 247, 252)-net over F₃, using

3¹ times duplication [i] based on digital (172, 246, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 82, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(247−74, 247, 536)-Net over F₃ — Digital

Digital (173, 247, 536)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−74, 247, 11183)-Net in Base 3 — Upper bound on s

There is no (173, 247, 11184)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7075 446367 393854 685167 381237 921148 596463 500216 003483 709881 449271 643940 991543 984530 195146 868773 766270 949011 886234 889569 > 3²⁴⁷ [i]