MinT - Best Known (181−56, 181, s)-Nets in Base 3

Best Known (181−56, 181, s)-Nets in Base 3

(181−56, 181, 192)-Net over F₃ — Constructive and digital

Digital (125, 181, 192)-net over F₃, using

3¹ times duplication [i] based on digital (124, 180, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 60, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(181−56, 181, 369)-Net over F₃ — Digital

Digital (125, 181, 369)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−56, 181, 6830)-Net in Base 3 — Upper bound on s

There is no (125, 181, 6831)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 577522 125675 821600 135859 855226 630736 400411 615559 771298 975750 112197 717570 351800 254153 > 3¹⁸¹ [i]