MinT - Best Known (12, 65, s)-Nets in Base 27

Best Known (12, 65, s)-Nets in Base 27

(12, 65, 96)-Net over F₂₇ — Constructive and digital

Digital (12, 65, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 65, 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]

(12, 65, 109)-Net over F₂₇ — Digital

Digital (12, 65, 109)-net over F₂₇, using

net from sequence [i] based on digital (12, 108)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 12 and N(F) ≥ 109, using
  - a curve from the manYPoints database [i]

(12, 65, 1340)-Net in Base 27 — Upper bound on s

There is no (12, 65, 1341)-net in base 27, because

1 times m-reduction [i] would yield (12, 64, 1341)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 40 708937 703671 431611 850493 770596 740760 300164 740292 954487 552490 448712 632745 740934 268123 726065 > 27⁶⁴ [i]