MinT - Best Known (178−54, 178, s)-Nets in Base 3

Best Known (178−54, 178, s)-Nets in Base 3

(178−54, 178, 204)-Net over F₃ — Constructive and digital

Digital (124, 178, 204)-net over F₃, using

3¹ times duplication [i] based on digital (123, 177, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 59, 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]

(178−54, 178, 387)-Net over F₃ — Digital

Digital (124, 178, 387)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−54, 178, 7609)-Net in Base 3 — Upper bound on s

There is no (124, 178, 7610)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 490158 318336 059956 086524 067129 369824 638233 892623 282308 883700 650559 068112 920381 191681 > 3¹⁷⁸ [i]