MinT - Best Known (126, 181, s)-Nets in Base 3

Best Known (126, 181, s)-Nets in Base 3

(126, 181, 204)-Net over F₃ — Constructive and digital

Digital (126, 181, 204)-net over F₃, using

3¹ times duplication [i] based on digital (125, 180, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 60, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(126, 181, 390)-Net over F₃ — Digital

Digital (126, 181, 390)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 181, 8256)-Net in Base 3 — Upper bound on s

There is no (126, 181, 8257)-net in base 3, because

1 times m-reduction [i] would yield (126, 180, 8257)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 304768 430926 437412 514776 018753 912462 905402 545486 406435 218672 806867 808728 687110 596283 > 3¹⁸⁰ [i]