MinT - Best Known (2, 2+24, s)-Nets in Base 8

Best Known (2, 2+24, s)-Nets in Base 8

(2, 2+24, 17)-Net over F₈ — Constructive and digital

Digital (2, 26, 17)-net over F₈, using

net from sequence [i] based on digital (2, 16)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 2 and N(F) ≥ 17, using
  - a function field by SÃ©mirat [i]

(2, 2+24, 18)-Net over F₈ — Digital

Digital (2, 26, 18)-net over F₈, using

net from sequence [i] based on digital (2, 17)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 2 and N(F) ≥ 18, using
  - sharp bound on the number of rational points on curves with genus 2 [i]

(2, 2+24, 24)-Net in Base 8 — Upper bound on s

There is no (2, 26, 25)-net in base 8, because

extracting embedded OOA [i] would yield OOA(8²⁶, 25, S₈, 2, 24), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 8 694214 891961 054030 925960 052736 / 27 969227 > 8²⁶ [i]