Best Known (128−110, 128, s)-Nets in Base 8
(128−110, 128, 65)-Net over F8 — Constructive and digital
Digital (18, 128, 65)-net over F8, using
- t-expansion [i] based on digital (14, 128, 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
(128−110, 128, 143)-Net in Base 8 — Upper bound on s
There is no (18, 128, 144)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(8128, 144, S8, 110), but
- the linear programming bound shows that M ≥ 6109 893966 434273 613815 828543 318095 703793 603744 881950 919851 825987 742070 359262 466307 770153 217353 472069 496822 008994 926770 763501 404160 / 124 535855 141787 > 8128 [i]