MinT - Best Known (2, s)-Sequences in Base 8

Best Known (2, s)-Sequences in Base 8

(2, 16)-Sequence over F₈ — Constructive and digital

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, 17)-Sequence over F₈ — Digital

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, 22)-Sequence in Base 8 — Upper bound on s

There is no (2, 23)-sequence in base 8, because

net from sequence [i] would yield (2, m, 24)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (2, 27, 24)-net in base 8, but
  - extracting embedded OOA [i] would yield OOA(8²⁷, 24, S₈, 2, 25), but
    - the linear programming bound for OOAs shows that MÂ â‰¥ 1329 818401 576092 092176 793600 / 513 > 8²⁷ [i]