MinT - Best Known (205−75, 205, s)-Nets in Base 3

Best Known (205−75, 205, s)-Nets in Base 3

(205−75, 205, 156)-Net over F₃ — Constructive and digital

Digital (130, 205, 156)-net over F₃, using

11 times m-reduction [i] based on digital (130, 216, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 108, 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]

(205−75, 205, 246)-Net over F₃ — Digital

Digital (130, 205, 246)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−75, 205, 3093)-Net in Base 3 — Upper bound on s

There is no (130, 205, 3094)-net in base 3, because

1 times m-reduction [i] would yield (130, 204, 3094)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 685709 973979 099651 139622 811421 037415 717308 399357 181534 591121 435604 234336 586575 866865 376888 284741 > 3²⁰⁴ [i]