Best Known (5, 5+13, s)-Nets in Base 128
(5, 5+13, 216)-Net over F128 — Constructive and digital
Digital (5, 18, 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+13, 227)-Net over F128 — Digital
Digital (5, 18, 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+13, 259)-Net in Base 128 — Constructive
(5, 18, 259)-net in base 128, using
- 6 times m-reduction [i] based on (5, 24, 259)-net in base 128, using
- base change [i] based on digital (2, 21, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 21, 259)-net over F256, using
(5, 5+13, 321)-Net in Base 128
(5, 18, 321)-net in base 128, using
- 6 times m-reduction [i] based on (5, 24, 321)-net in base 128, using
- base change [i] based on digital (2, 21, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 21, 321)-net over F256, using
(5, 5+13, 22018)-Net in Base 128 — Upper bound on s
There is no (5, 18, 22019)-net in base 128, because
- 1 times m-reduction [i] would yield (5, 17, 22019)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 664625 189978 374757 032405 004509 801856 > 12817 [i]