MinT - Best Known (130, 130+65, s)-Nets in Base 3

Best Known (130, 130+65, s)-Nets in Base 3

(130, 130+65, 162)-Net over F₃ — Constructive and digital

Digital (130, 195, 162)-net over F₃, using

1 times m-reduction [i] based on digital (130, 196, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 98, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(130, 130+65, 312)-Net over F₃ — Digital

Digital (130, 195, 312)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+65, 4962)-Net in Base 3 — Upper bound on s

There is no (130, 195, 4963)-net in base 3, because

1 times m-reduction [i] would yield (130, 194, 4963)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 366 692895 257207 803081 622864 235064 895150 510167 493295 220620 543833 968752 197815 852584 177500 235201 > 3¹⁹⁴ [i]