Best Known (25−20, 25, s)-Nets in Base 128
(25−20, 25, 216)-Net over F128 — Constructive and digital
Digital (5, 25, 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
(25−20, 25, 227)-Net over F128 — Digital
Digital (5, 25, 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
(25−20, 25, 258)-Net in Base 128 — Constructive
(5, 25, 258)-net in base 128, using
- 7 times m-reduction [i] based on (5, 32, 258)-net in base 128, using
- base change [i] based on digital (1, 28, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 28, 258)-net over F256, using
(25−20, 25, 289)-Net in Base 128
(5, 25, 289)-net in base 128, using
- 7 times m-reduction [i] based on (5, 32, 289)-net in base 128, using
- base change [i] based on digital (1, 28, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- base change [i] based on digital (1, 28, 289)-net over F256, using
(25−20, 25, 6605)-Net in Base 128 — Upper bound on s
There is no (5, 25, 6606)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 47936 746745 715151 843336 052222 213405 141067 030841 593006 > 12825 [i]