MinT - Best Known (163, 163+72, s)-Nets in Base 3

Best Known (163, 163+72, s)-Nets in Base 3

(163, 163+72, 228)-Net over F₃ — Constructive and digital

Digital (163, 235, 228)-net over F₃, using

3¹ times duplication [i] based on digital (162, 234, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 78, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(163, 163+72, 478)-Net over F₃ — Digital

Digital (163, 235, 478)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+72, 9259)-Net in Base 3 — Upper bound on s

There is no (163, 235, 9260)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13312 782299 800492 897880 754616 162167 531330 095549 890948 201502 460145 381289 481779 399627 311394 916231 514522 227643 206273 > 3²³⁵ [i]