Best Known (159−150, 159, s)-Nets in Base 8
(159−150, 159, 45)-Net over F8 — Constructive and digital
Digital (9, 159, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
(159−150, 159, 79)-Net over F8 — Upper bound on s (digital)
There is no digital (9, 159, 80)-net over F8, because
- 86 times m-reduction [i] would yield digital (9, 73, 80)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(873, 80, F8, 64) (dual of [80, 7, 65]-code), but
- residual code [i] would yield linear OA(89, 15, F8, 8) (dual of [15, 6, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(89, 15, F8, 8) (dual of [15, 6, 9]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(873, 80, F8, 64) (dual of [80, 7, 65]-code), but
(159−150, 159, 80)-Net in Base 8 — Upper bound on s
There is no (9, 159, 81)-net in base 8, because
- extracting embedded OOA [i] would yield OOA(8159, 81, S8, 2, 150), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 78 043713 757899 805784 539930 744829 157643 714953 566624 278771 478923 990634 293470 494140 503007 652576 587299 278995 673278 035165 572386 199391 982207 132657 254400 / 151 > 8159 [i]