MinT - Best Known (62−48, 62, s)-Nets in Base 27

Best Known (62−48, 62, s)-Nets in Base 27

(62−48, 62, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 62, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 62, 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]

(62−48, 62, 136)-Net over F₂₇ — Digital

Digital (14, 62, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 62, 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]

(62−48, 62, 1867)-Net in Base 27 — Upper bound on s

There is no (14, 62, 1868)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 56064 174727 548462 913415 173655 962665 089464 336007 432284 479527 970016 273803 497038 471002 285633 > 27⁶² [i]