Best Known (71−63, 71, s)-Nets in Base 128
(71−63, 71, 216)-Net over F128 — Constructive and digital
Digital (8, 71, 216)-net over F128, using
- t-expansion [i] based on digital (5, 71, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(71−63, 71, 276)-Net over F128 — Digital
Digital (8, 71, 276)-net over F128, using
- net from sequence [i] based on digital (8, 275)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 8 and N(F) ≥ 276, using
(71−63, 71, 5588)-Net in Base 128 — Upper bound on s
There is no (8, 71, 5589)-net in base 128, because
- 1 times m-reduction [i] would yield (8, 70, 5589)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 3212 944204 222274 060205 024078 667401 935171 339314 043172 686795 025104 936335 635913 142506 957320 040337 155749 119339 358653 775987 012903 759882 337172 260003 385152 > 12870 [i]