Best Known (5, 5+49, s)-Nets in Base 128
(5, 5+49, 216)-Net over F128 — Constructive and digital
Digital (5, 54, 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
(5, 5+49, 227)-Net over F128 — Digital
Digital (5, 54, 227)-net over F128, using
- net from sequence [i] based on digital (5, 226)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 227, using
(5, 5+49, 3463)-Net in Base 128 — Upper bound on s
There is no (5, 54, 3464)-net in base 128, because
- 1 times m-reduction [i] would yield (5, 53, 3464)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 4825 505676 696709 270170 943591 446298 199337 077864 783740 199709 452191 358615 554655 469842 665605 508986 522054 364590 511312 > 12853 [i]