MinT - Best Known (207−75, 207, s)-Nets in Base 3

Best Known (207−75, 207, s)-Nets in Base 3

(207−75, 207, 156)-Net over F₃ — Constructive and digital

Digital (132, 207, 156)-net over F₃, using

13 times m-reduction [i] based on digital (132, 220, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 110, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(207−75, 207, 256)-Net over F₃ — Digital

Digital (132, 207, 256)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−75, 207, 3284)-Net in Base 3 — Upper bound on s

There is no (132, 207, 3285)-net in base 3, because

1 times m-reduction [i] would yield (132, 206, 3285)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 194 059499 901642 979752 932421 288342 018592 714479 809618 876527 629971 129664 073406 602369 237144 576671 239995 > 3²⁰⁶ [i]