Best Known (71−38, 71, s)-Nets in Base 128
(71−38, 71, 504)-Net over F128 — Constructive and digital
Digital (33, 71, 504)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (5, 24, 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
- digital (9, 47, 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 (5, 24, 216)-net over F128, using
(71−38, 71, 547)-Net in Base 128 — Constructive
(33, 71, 547)-net in base 128, using
- (u, u+v)-construction [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
- digital (9, 47, 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
- (5, 24, 259)-net in base 128, using
(71−38, 71, 1294)-Net over F128 — Digital
Digital (33, 71, 1294)-net over F128, using
(71−38, 71, 4674356)-Net in Base 128 — Upper bound on s
There is no (33, 71, 4674357)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 409173 891242 901828 018777 315869 613582 963456 634170 982641 114032 693072 832287 365190 589141 683230 724592 585183 428713 771040 752886 193238 673856 467485 442203 227892 > 12871 [i]