MinT - Best Known (97−81, 97, s)-Nets in Base 27

Best Known (97−81, 97, s)-Nets in Base 27

(97−81, 97, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 97, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 97, 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]

(97−81, 97, 144)-Net over F₂₇ — Digital

Digital (16, 97, 144)-net over F₂₇, using

net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
  - a curve from the manYPoints database [i]

(97−81, 97, 1631)-Net in Base 27 — Upper bound on s

There is no (16, 97, 1632)-net in base 27, because

1 times m-reduction [i] would yield (16, 96, 1632)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 261810 557250 404640 439039 656063 518942 737423 737767 459344 924846 095757 619611 277383 891229 068514 972842 129762 254796 443501 868391 656102 450125 461505 > 27⁹⁶ [i]