MinT - Best Known (187−57, 187, s)-Nets in Base 3

Best Known (187−57, 187, s)-Nets in Base 3

(187−57, 187, 204)-Net over F₃ — Constructive and digital

Digital (130, 187, 204)-net over F₃, using

3¹ times duplication [i] based on digital (129, 186, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 62, 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]

(187−57, 187, 397)-Net over F₃ — Digital

Digital (130, 187, 397)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−57, 187, 8317)-Net in Base 3 — Upper bound on s

There is no (130, 187, 8318)-net in base 3, because

1 times m-reduction [i] would yield (130, 186, 8318)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55630 131316 344507 451841 339801 791748 844998 037288 545167 527213 334300 227712 194552 902847 759737 > 3¹⁸⁶ [i]