Best Known (10, 10+137, s)-Nets in Base 8
(10, 10+137, 46)-Net over F8 — Constructive and digital
Digital (10, 147, 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, 10+137, 88)-Net in Base 8 — Upper bound on s
There is no (10, 147, 89)-net in base 8, because
- 68 times m-reduction [i] would yield (10, 79, 89)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(879, 89, S8, 69), but
- the linear programming bound shows that M ≥ 65 600614 468436 793327 664966 251603 548180 144825 093020 806068 320527 896711 603979 026432 / 245 278125 > 879 [i]
- extracting embedded orthogonal array [i] would yield OA(879, 89, S8, 69), but