MinT - Best Known (86−73, 86, s)-Nets in Base 27

Best Known (86−73, 86, s)-Nets in Base 27

(86−73, 86, 96)-Net over F₂₇ — Constructive and digital

Digital (13, 86, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 86, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(86−73, 86, 136)-Net over F₂₇ — Digital

Digital (13, 86, 136)-net over F₂₇, using

net from sequence [i] based on digital (13, 135)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 13 and N(F) ≥ 136, using
  - a curve from the manYPoints database [i]

(86−73, 86, 1297)-Net in Base 27 — Upper bound on s

There is no (13, 86, 1298)-net in base 27, because

1 times m-reduction [i] would yield (13, 85, 1298)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 46 936656 579081 912030 600257 792193 893460 348453 149528 415928 083296 808278 457890 326058 733205 325887 940944 687885 823314 039526 322537 > 27⁸⁵ [i]