MinT - Best Known (88−75, 88, s)-Nets in Base 27

Best Known (88−75, 88, s)-Nets in Base 27

(88−75, 88, 96)-Net over F₂₇ — Constructive and digital

Digital (13, 88, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 88, 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]

(88−75, 88, 136)-Net over F₂₇ — Digital

Digital (13, 88, 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]

(88−75, 88, 1288)-Net in Base 27 — Upper bound on s

There is no (13, 88, 1289)-net in base 27, because

1 times m-reduction [i] would yield (13, 87, 1289)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 34211 951106 232293 676879 426437 955864 081102 955885 454719 821320 446907 529859 551557 014112 934533 157444 446862 811183 250254 822509 285691 > 27⁸⁷ [i]