MinT - Best Known (53−46, 53, s)-Nets in Base 8

Best Known (53−46, 53, s)-Nets in Base 8

(53−46, 53, 34)-Net over F₈ — Constructive and digital

Digital (7, 53, 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]

(53−46, 53, 90)-Net in Base 8 — Upper bound on s

There is no (7, 53, 91)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵³, 91, S₈, 46), but
- the linear programming bound shows that MÂ â‰¥ 20 208449 323021 384919 248834 132521 231880 298704 300690 132338 929765 327670 766747 534185 163562 942464 / 26 326437 187405 123176 982870 223897 421859 220957 > 8⁵³ [i]