MinT - Best Known (8, 8+48, s)-Nets in Base 27

Best Known (8, 8+48, s)-Nets in Base 27

(8, 8+48, 84)-Net over F₂₇ — Constructive and digital

Digital (8, 56, 84)-net over F₂₇, using

net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
  - a function field by SÃ©mirat [i]

(8, 8+48, 92)-Net over F₂₇ — Digital

Digital (8, 56, 92)-net over F₂₇, using

net from sequence [i] based on digital (8, 91)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 92, using
  - a curve from the manYPoints database [i]

(8, 8+48, 812)-Net in Base 27 — Upper bound on s

There is no (8, 56, 813)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 146 676191 740521 936695 756253 423187 079431 787448 402896 340218 030580 917535 593837 992161 > 27⁵⁶ [i]