MinT - Best Known (130, 130+51, s)-Nets in Base 3

Best Known (130, 130+51, s)-Nets in Base 3

(130, 130+51, 264)-Net over F₃ — Constructive and digital

Digital (130, 181, 264)-net over F₃, using

3¹ times duplication [i] based on digital (129, 180, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 60, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(130, 130+51, 502)-Net over F₃ — Digital

Digital (130, 181, 502)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+51, 13838)-Net in Base 3 — Upper bound on s

There is no (130, 181, 13839)-net in base 3, because

1 times m-reduction [i] would yield (130, 180, 13839)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 192498 719583 211042 977041 798376 456028 474863 475042 025521 966820 163696 100483 092573 861359 > 3¹⁸⁰ [i]