Best Known (7, 72, s)-Nets in Base 128
(7, 72, 216)-Net over F128 — Constructive and digital
Digital (7, 72, 216)-net over F128, using
- t-expansion [i] based on digital (5, 72, 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
(7, 72, 262)-Net over F128 — Digital
Digital (7, 72, 262)-net over F128, using
- net from sequence [i] based on digital (7, 261)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 7 and N(F) ≥ 262, using
(7, 72, 4753)-Net in Base 128 — Upper bound on s
There is no (7, 72, 4754)-net in base 128, because
- 1 times m-reduction [i] would yield (7, 71, 4754)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 410567 298724 984418 928805 774948 250751 558906 181861 221596 940619 973297 411129 693301 807151 368776 552581 424902 853890 245334 095050 191742 210377 622847 966447 712708 > 12871 [i]