Best Known (5, 37, s)-Nets in Base 8
(5, 37, 28)-Net over F8 — Constructive and digital
Digital (5, 37, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
(5, 37, 29)-Net over F8 — Digital
Digital (5, 37, 29)-net over F8, using
- net from sequence [i] based on digital (5, 28)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 29, using
(5, 37, 67)-Net over F8 — Upper bound on s (digital)
There is no digital (5, 37, 68)-net over F8, because
- extracting embedded orthogonal array [i] would yield linear OA(837, 68, F8, 32) (dual of [68, 31, 33]-code), but
- residual code [i] would yield OA(85, 35, S8, 4), but
- the linear programming bound shows that M ≥ 1 306624 / 39 > 85 [i]
- residual code [i] would yield OA(85, 35, S8, 4), but
(5, 37, 88)-Net in Base 8 — Upper bound on s
There is no (5, 37, 89)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(837, 89, S8, 32), but
- the linear programming bound shows that M ≥ 42 628902 653755 722532 705789 417561 961232 422700 620787 643894 825054 371840 / 15458 508164 091799 529005 040361 729673 > 837 [i]