MinT - Best Known (187−79, 187, s)-Nets in Base 3

Best Known (187−79, 187, s)-Nets in Base 3

(187−79, 187, 128)-Net over F₃ — Constructive and digital

Digital (108, 187, 128)-net over F₃, using

3 times m-reduction [i] based on digital (108, 190, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 95, 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]

(187−79, 187, 151)-Net over F₃ — Digital

Digital (108, 187, 151)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−79, 187, 1413)-Net in Base 3 — Upper bound on s

There is no (108, 187, 1414)-net in base 3, because

1 times m-reduction [i] would yield (108, 186, 1414)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56003 593635 913165 735169 115196 287171 439521 050274 726940 458506 381512 001732 156054 869086 368985 > 3¹⁸⁶ [i]