MinT - Best Known (130, 130+89, s)-Nets in Base 3

Best Known (130, 130+89, s)-Nets in Base 3

(130, 130+89, 148)-Net over F₃ — Constructive and digital

Digital (130, 219, 148)-net over F₃, using

7 times m-reduction [i] based on digital (130, 226, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 113, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(130, 130+89, 193)-Net over F₃ — Digital

Digital (130, 219, 193)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+89, 1951)-Net in Base 3 — Upper bound on s

There is no (130, 219, 1952)-net in base 3, because

1 times m-reduction [i] would yield (130, 218, 1952)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104 532344 710845 309336 751903 754494 826569 122800 272170 586275 366315 968919 915965 181037 873948 451070 553143 699201 > 3²¹⁸ [i]