Best Known (69−54, 69, s)-Nets in Base 8
(69−54, 69, 65)-Net over F8 — Constructive and digital
Digital (15, 69, 65)-net over F8, using
- t-expansion [i] based on digital (14, 69, 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
(69−54, 69, 295)-Net in Base 8 — Upper bound on s
There is no (15, 69, 296)-net in base 8, because
- 3 times m-reduction [i] would yield (15, 66, 296)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(866, 296, S8, 51), but
- the linear programming bound shows that M ≥ 1 250062 958837 561183 624404 744244 192700 439017 944864 767705 236229 106710 888395 390839 850805 321385 337484 514454 170810 392090 648828 600419 191095 296000 / 3 096891 109413 013981 634976 757753 456870 522002 446974 025728 410339 087894 301101 500579 > 866 [i]
- extracting embedded orthogonal array [i] would yield OA(866, 296, S8, 51), but