Best Known (10, 69, s)-Nets in Base 8
(10, 69, 46)-Net over F8 — Constructive and digital
Digital (10, 69, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
(10, 69, 126)-Net in Base 8 — Upper bound on s
There is no (10, 69, 127)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(869, 127, S8, 59), but
- the linear programming bound shows that M ≥ 367 365295 442645 166363 532295 756030 027773 773538 863524 245424 318274 427291 601727 601050 099536 112345 789056 665417 582338 205420 843380 342027 204898 947711 934175 500973 375488 / 1 685725 206919 552750 685794 656985 180843 124798 410394 767701 211697 086005 045309 894199 011500 352326 947803 > 869 [i]