MinT - Best Known (70−55, 70, s)-Nets in Base 27

Best Known (70−55, 70, s)-Nets in Base 27

(70−55, 70, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 70, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 70, 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]

(70−55, 70, 136)-Net over F₂₇ — Digital

Digital (15, 70, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 70, 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]

(70−55, 70, 1897)-Net in Base 27 — Upper bound on s

There is no (15, 70, 1898)-net in base 27, because

1 times m-reduction [i] would yield (15, 69, 1898)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 585 550564 525597 005241 589776 174985 597904 559981 990901 517304 632867 361091 059315 881779 160401 528351 347121 > 27⁶⁹ [i]