Best Known (7, 7+28, s)-Nets in Base 128
(7, 7+28, 216)-Net over F128 — Constructive and digital
Digital (7, 35, 216)-net over F128, using
- t-expansion [i] based on digital (5, 35, 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, 7+28, 259)-Net in Base 128 — Constructive
(7, 35, 259)-net in base 128, using
- 5 times m-reduction [i] based on (7, 40, 259)-net in base 128, using
- base change [i] based on digital (2, 35, 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, 35, 259)-net over F256, using
(7, 7+28, 262)-Net over F128 — Digital
Digital (7, 35, 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, 7+28, 321)-Net in Base 128
(7, 35, 321)-net in base 128, using
- 5 times m-reduction [i] based on (7, 40, 321)-net in base 128, using
- base change [i] based on digital (2, 35, 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, 35, 321)-net over F256, using
(7, 7+28, 8817)-Net in Base 128 — Upper bound on s
There is no (7, 35, 8818)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 56 569261 297260 735358 492294 480166 393091 895154 909438 148512 960702 176493 458488 > 12835 [i]