MinT - Best Known (93−69, 93, s)-Nets in Base 27

Best Known (93−69, 93, s)-Nets in Base 27

(93−69, 93, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 93, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 93, 114)-net over F₂₇, using
- net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
    - an explicitly constructive algebraic function field [i]

(93−69, 93, 208)-Net over F₂₇ — Digital

Digital (24, 93, 208)-net over F₂₇, using

net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
  - an algebraic function field by Beelen and Pellikaan [i]

(93−69, 93, 3869)-Net in Base 27 — Upper bound on s

There is no (24, 93, 3870)-net in base 27, because

1 times m-reduction [i] would yield (24, 92, 3870)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 488452 940105 257680 716471 979265 964578 616782 367206 894174 345221 602461 360695 171370 730064 589243 537669 316194 140797 423920 750951 529617 265725 > 27⁹² [i]