MinT - Best Known (51−44, 51, s)-Nets in Base 8

Best Known (51−44, 51, s)-Nets in Base 8

(51−44, 51, 34)-Net over F₈ — Constructive and digital

Digital (7, 51, 34)-net over F₈, using

net from sequence [i] based on digital (7, 33)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
  - a function field by SÃ©mirat [i]

(51−44, 51, 102)-Net in Base 8 — Upper bound on s

There is no (7, 51, 103)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵¹, 103, S₈, 44), but
- the linear programming bound shows that MÂ â‰¥ 1 086279 357773 661309 243999 533972 009965 902387 336466 404571 186324 986903 448185 153639 397593 248782 352384 / 93 742712 619418 183840 904606 442617 327913 950851 439827 > 8⁵¹ [i]