Best Known (66−35, 66, s)-Nets in Base 128
(66−35, 66, 504)-Net over F128 — Constructive and digital
Digital (31, 66, 504)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (5, 22, 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, 44, 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, 22, 216)-net over F128, using
(66−35, 66, 547)-Net in Base 128 — Constructive
(31, 66, 547)-net in base 128, using
- (u, u+v)-construction [i] based on
- (5, 22, 259)-net in base 128, using
- 2 times m-reduction [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
- 2 times m-reduction [i] based on (5, 24, 259)-net in base 128, using
- digital (9, 44, 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, 22, 259)-net in base 128, using
(66−35, 66, 1330)-Net over F128 — Digital
Digital (31, 66, 1330)-net over F128, using
(66−35, 66, 6443476)-Net in Base 128 — Upper bound on s
There is no (31, 66, 6443477)-net in base 128, because
- 1 times m-reduction [i] would yield (31, 65, 6443477)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 93035 536390 007185 071933 004476 460395 315744 762434 610185 532653 047430 113896 592612 270554 349098 172629 936610 550592 729838 240526 255614 380125 391292 > 12865 [i]