Best Known (8, 8+106, s)-Nets in Base 16
(8, 8+106, 65)-Net over F16 — Constructive and digital
Digital (8, 114, 65)-net over F16, using
- t-expansion [i] based on digital (6, 114, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(8, 8+106, 189)-Net in Base 16 — Upper bound on s
There is no (8, 114, 190)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16114, 190, S16, 106), but
- the linear programming bound shows that M ≥ 5240 788397 161506 511762 002675 491507 442049 922873 457937 930838 753868 236818 053215 853720 121795 949388 613401 489627 433647 487080 525503 374823 125370 930009 540408 892618 107175 914498 797677 945186 315633 465996 210086 084608 / 26414 595265 534333 375964 029682 733724 777422 969548 110568 431508 757949 > 16114 [i]