Best Known (68−38, 68, s)-Nets in Base 128
(68−38, 68, 438)-Net over F128 — Constructive and digital
Digital (30, 68, 438)-net over F128, using
- 2 times m-reduction [i] based on digital (30, 70, 438)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 21, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (9, 49, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- digital (1, 21, 150)-net over F128, using
- (u, u+v)-construction [i] based on
(68−38, 68, 516)-Net in Base 128 — Constructive
(30, 68, 516)-net in base 128, using
- (u, u+v)-construction [i] based on
- (4, 23, 258)-net in base 128, using
- 1 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
- 1 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- (7, 45, 258)-net in base 128, using
- 3 times m-reduction [i] based on (7, 48, 258)-net in base 128, using
- base change [i] based on digital (1, 42, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- base change [i] based on digital (1, 42, 258)-net over F256, using
- 3 times m-reduction [i] based on (7, 48, 258)-net in base 128, using
- (4, 23, 258)-net in base 128, using
(68−38, 68, 879)-Net over F128 — Digital
Digital (30, 68, 879)-net over F128, using
(68−38, 68, 2172718)-Net in Base 128 — Upper bound on s
There is no (30, 68, 2172719)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 195109 540960 054447 288454 661762 668313 698074 444025 898980 896140 406164 820300 605880 008082 106687 115199 625877 312793 405278 584070 594316 805668 841866 372200 > 12868 [i]