Best Known (76−60, 76, s)-Nets in Base 8
(76−60, 76, 65)-Net over F8 — Constructive and digital
Digital (16, 76, 65)-net over F8, using
- t-expansion [i] based on digital (14, 76, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(76−60, 76, 299)-Net in Base 8 — Upper bound on s
There is no (16, 76, 300)-net in base 8, because
- 2 times m-reduction [i] would yield (16, 74, 300)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(874, 300, S8, 58), but
- the linear programming bound shows that M ≥ 9484 880837 890886 438207 523908 826636 321312 911261 221645 649646 026350 563089 163931 675158 932013 232120 501960 989670 851342 786972 645143 430967 516677 902360 796305 817600 / 1350 585561 592555 221400 173603 375830 017309 031610 937317 207818 710872 803762 996430 646282 904581 > 874 [i]
- extracting embedded orthogonal array [i] would yield OA(874, 300, S8, 58), but