MinT - Best Known (230−66, 230, s)-Nets in Base 3

Best Known (230−66, 230, s)-Nets in Base 3

(230−66, 230, 282)-Net over F₃ — Constructive and digital

Digital (164, 230, 282)-net over F₃, using

1 times m-reduction [i] based on digital (164, 231, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 77, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(230−66, 230, 579)-Net over F₃ — Digital

Digital (164, 230, 579)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−66, 230, 13889)-Net in Base 3 — Upper bound on s

There is no (164, 230, 13890)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 694046 903473 663315 026559 378722 576493 175900 366512 759397 012578 759783 063064 068427 393102 488356 747618 483714 262341 > 3²³⁰ [i]