Best Known (17−13, 17, s)-Nets in Base 128
(17−13, 17, 192)-Net over F128 — Constructive and digital
Digital (4, 17, 192)-net over F128, using
- t-expansion [i] based on digital (3, 17, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
(17−13, 17, 215)-Net over F128 — Digital
Digital (4, 17, 215)-net over F128, using
- net from sequence [i] based on digital (4, 214)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 4 and N(F) ≥ 215, using
(17−13, 17, 258)-Net in Base 128 — Constructive
(4, 17, 258)-net in base 128, using
- 7 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- base change [i] based on digital (1, 21, 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, 21, 258)-net over F256, using
(17−13, 17, 289)-Net in Base 128
(4, 17, 289)-net in base 128, using
- 7 times m-reduction [i] based on (4, 24, 289)-net in base 128, using
- base change [i] based on digital (1, 21, 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, 21, 289)-net over F256, using
(17−13, 17, 9806)-Net in Base 128 — Upper bound on s
There is no (4, 17, 9807)-net in base 128, because
- 1 times m-reduction [i] would yield (4, 16, 9807)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 5192 584414 415867 173631 760954 864395 > 12816 [i]