Best Known (42−37, 42, s)-Nets in Base 128
(42−37, 42, 216)-Net over F128 — Constructive and digital
Digital (5, 42, 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
(42−37, 42, 227)-Net over F128 — Digital
Digital (5, 42, 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
(42−37, 42, 3741)-Net in Base 128 — Upper bound on s
There is no (5, 42, 3742)-net in base 128, because
- 1 times m-reduction [i] would yield (5, 41, 3742)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 248 896203 783880 093830 505289 923041 429744 306617 699825 995871 031600 745315 814864 451446 645210 > 12841 [i]