MinT - Best Known (76−65, 76, s)-Nets in Base 8

Best Known (76−65, 76, s)-Nets in Base 8

(76−65, 76, 48)-Net over F₈ — Constructive and digital

Digital (11, 76, 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]

(76−65, 76, 128)-Net in Base 8 — Upper bound on s

There is no (11, 76, 129)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁷⁶, 129, S₈, 65), but
- the linear programming bound shows that MÂ â‰¥ 29406 598024 374807 124650 979976 625091 532916 199802 339696 477612 503350 598258 035469 687880 220229 763495 954432 618315 913978 809471 637560 095460 687729 625421 534803 787776 / 67 514539 915233 845508 272807 879200 930028 726901 711025 332188 644961 182227 262629 929896 667531 > 8⁷⁶ [i]