MinT - Best Known (130, 130+85, s)-Nets in Base 3

Best Known (130, 130+85, s)-Nets in Base 3

(130, 130+85, 156)-Net over F₃ — Constructive and digital

Digital (130, 215, 156)-net over F₃, using

1 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]

(130, 130+85, 206)-Net over F₃ — Digital

Digital (130, 215, 206)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+85, 2186)-Net in Base 3 — Upper bound on s

There is no (130, 215, 2187)-net in base 3, because

1 times m-reduction [i] would yield (130, 214, 2187)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 286761 779627 093116 411291 538931 069235 688816 822001 973611 219120 555682 415365 038088 269647 212369 244820 369957 > 3²¹⁴ [i]