Best Known (71−39, 71, s)-Nets in Base 128
(71−39, 71, 480)-Net over F128 — Constructive and digital
Digital (32, 71, 480)-net over F128, using
- 1 times m-reduction [i] based on digital (32, 72, 480)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 23, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-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 (3, 23, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(71−39, 71, 546)-Net in Base 128 — Constructive
(32, 71, 546)-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
- digital (9, 48, 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
- (4, 23, 258)-net in base 128, using
(71−39, 71, 1043)-Net over F128 — Digital
Digital (32, 71, 1043)-net over F128, using
(71−39, 71, 3620894)-Net in Base 128 — Upper bound on s
There is no (32, 71, 3620895)-net in base 128, because
- 1 times m-reduction [i] would yield (32, 70, 3620895)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 3196 683357 935302 067996 157765 388234 613598 442678 991471 220901 002300 623055 944580 116313 999667 072083 504309 948212 695432 490989 154152 002192 181700 023060 889500 > 12870 [i]