MinT - Best Known (12, 12+70, s)-Nets in Base 27

Best Known (12, 12+70, s)-Nets in Base 27

(12, 12+70, 96)-Net over F₂₇ — Constructive and digital

Digital (12, 82, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 82, 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, 12+70, 109)-Net over F₂₇ — Digital

Digital (12, 82, 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, 12+70, 1188)-Net in Base 27 — Upper bound on s

There is no (12, 82, 1189)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2361 404284 015070 336992 956009 670952 433009 793596 648778 803776 536871 916321 182040 233612 802642 000376 482701 139929 803665 912147 > 27⁸² [i]