Best Known (23, 23+∞, s)-Nets in Base 8
(23, 23+∞, 65)-Net over F8 — Constructive and digital
Digital (23, m, 65)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (23, 64)-sequence over F8, using
- t-expansion [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
- t-expansion [i] based on digital (14, 64)-sequence over F8, using
(23, 23+∞, 76)-Net over F8 — Digital
Digital (23, m, 76)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (23, 75)-sequence over F8, using
- t-expansion [i] based on digital (20, 75)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 20 and N(F) ≥ 76, using
- t-expansion [i] based on digital (20, 75)-sequence over F8, using
(23, 23+∞, 182)-Net in Base 8 — Upper bound on s
There is no (23, m, 183)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (23, 363, 183)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8363, 183, S8, 2, 340), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 493751 205676 606832 657637 388003 341351 342351 984601 249759 303922 831140 906849 978490 894135 364952 776388 077492 317102 964182 918059 870391 017703 287924 391838 953561 052929 408714 392469 141974 975760 213967 734352 914224 009940 361286 312896 587817 539484 210967 572044 974784 288658 049638 355661 532419 763860 122064 288222 480274 006045 437296 761179 689817 015542 874112 / 341 > 8363 [i]
- extracting embedded OOA [i] would yield OOA(8363, 183, S8, 2, 340), but