Best Known (27−22, 27, s)-Nets in Base 128
(27−22, 27, 216)-Net over F128 — Constructive and digital
Digital (5, 27, 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
(27−22, 27, 227)-Net over F128 — Digital
Digital (5, 27, 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
(27−22, 27, 258)-Net in Base 128 — Constructive
(5, 27, 258)-net in base 128, using
- 5 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
(27−22, 27, 289)-Net in Base 128
(5, 27, 289)-net in base 128, using
- 5 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
(27−22, 27, 5742)-Net in Base 128 — Upper bound on s
There is no (5, 27, 5743)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 786 032976 121145 819361 566559 913647 850106 115494 884553 194564 > 12827 [i]