MinT - Best Known (102, 102+72, s)-Nets in Base 3

Best Known (102, 102+72, s)-Nets in Base 3

(102, 102+72, 128)-Net over F₃ — Constructive and digital

Digital (102, 174, 128)-net over F₃, using

4 times m-reduction [i] based on digital (102, 178, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 89, 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]

(102, 102+72, 151)-Net over F₃ — Digital

Digital (102, 174, 151)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+72, 1409)-Net in Base 3 — Upper bound on s

There is no (102, 174, 1410)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 105513 880950 808580 177941 243921 742937 966932 964157 837134 179247 670670 335125 041501 821545 > 3¹⁷⁴ [i]