MinT - Best Known (11, 80, s)-Nets in Base 27

Best Known (11, 80, s)-Nets in Base 27

(11, 80, 96)-Net over F₂₇ — Constructive and digital

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]

(11, 80, 100)-Net over F₂₇ — Digital

Digital (11, 80, 100)-net over F₂₇, using

net from sequence [i] based on digital (11, 99)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 100, using
  - a curve from the manYPoints database [i]

(11, 80, 1084)-Net in Base 27 — Upper bound on s

There is no (11, 80, 1085)-net in base 27, because

1 times m-reduction [i] would yield (11, 79, 1085)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 121078 867260 877132 848412 053612 072820 988124 428811 092047 739692 535981 069567 965075 206862 811436 598424 557722 089184 647505 > 27⁷⁹ [i]