MinT - Best Known (77−66, 77, s)-Nets in Base 8

Best Known (77−66, 77, s)-Nets in Base 8

(77−66, 77, 48)-Net over F₈ — Constructive and digital

Digital (11, 77, 48)-net over F₈, using

net from sequence [i] based on digital (11, 47)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
  - a function field by SÃ©mirat [i]

(77−66, 77, 122)-Net in Base 8 — Upper bound on s

There is no (11, 77, 123)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁷⁷, 123, S₈, 66), but
- the linear programming bound shows that MÂ â‰¥ 1129 230260 229759 489111 139458 787937 792138 528773 327217 859367 183222 664699 366840 063192 450689 953772 735193 436444 565207 193541 640361 869312 / 321114 601876 460958 369221 611200 006781 071977 768319 383141 301795 > 8⁷⁷ [i]