MinT - Best Known (180−51, 180, s)-Nets in Base 3

Best Known (180−51, 180, s)-Nets in Base 3

(180−51, 180, 264)-Net over F₃ — Constructive and digital

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]

(180−51, 180, 490)-Net over F₃ — Digital

Digital (129, 180, 490)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−51, 180, 13242)-Net in Base 3 — Upper bound on s

There is no (129, 180, 13243)-net in base 3, because

1 times m-reduction [i] would yield (129, 179, 13243)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25 398972 890605 540748 697362 649859 267111 840005 439785 833927 983323 976474 842392 409397 986951 > 3¹⁷⁹ [i]