Best Known (70−65, 70, s)-Nets in Base 128
(70−65, 70, 216)-Net over F128 — Constructive and digital
Digital (5, 70, 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
(70−65, 70, 227)-Net over F128 — Digital
Digital (5, 70, 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
(70−65, 70, 3447)-Net in Base 128 — Upper bound on s
There is no (5, 70, 3448)-net in base 128, because
- 13 times m-reduction [i] would yield (5, 57, 3448)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 1 292786 971607 867841 675189 158041 192679 960611 914850 254940 704269 950622 106891 470459 066465 914243 847053 416319 142113 082596 363324 > 12857 [i]