MinT - Best Known (231−67, 231, s)-Nets in Base 3

Best Known (231−67, 231, s)-Nets in Base 3

(231−67, 231, 282)-Net over F₃ — Constructive and digital

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]

(231−67, 231, 561)-Net over F₃ — Digital

Digital (164, 231, 561)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−67, 231, 13889)-Net in Base 3 — Upper bound on s

There is no (164, 231, 13890)-net in base 3, because

1 times m-reduction [i] would yield (164, 230, 13890)-net in base 3, but
- 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]