MinT - Best Known (80−63, 80, s)-Nets in Base 27

Best Known (80−63, 80, s)-Nets in Base 27

(80−63, 80, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 80, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 80, 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]

(80−63, 80, 144)-Net over F₂₇ — Digital

Digital (17, 80, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 80, 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]

(80−63, 80, 2105)-Net in Base 27 — Upper bound on s

There is no (17, 80, 2106)-net in base 27, because

1 times m-reduction [i] would yield (17, 79, 2106)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 120033 925247 888313 383814 619794 524938 695593 886040 601135 288508 791905 959784 239396 142065 654694 743780 174996 823568 035081 > 27⁷⁹ [i]