Best Known (77−43, 77, s)-Nets in Base 128
(77−43, 77, 480)-Net over F128 — Constructive and digital
Digital (34, 77, 480)-net over F128, using
- 1 times m-reduction [i] based on digital (34, 78, 480)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 25, 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, 53, 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, 25, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(77−43, 77, 545)-Net in Base 128 — Constructive
(34, 77, 545)-net in base 128, using
- 1281 times duplication [i] based on (33, 76, 545)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 24, 257)-net in base 128, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- digital (9, 52, 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
- (3, 24, 257)-net in base 128, using
- (u, u+v)-construction [i] based on
(77−43, 77, 970)-Net over F128 — Digital
Digital (34, 77, 970)-net over F128, using
(77−43, 77, 2889219)-Net in Base 128 — Upper bound on s
There is no (34, 77, 2889220)-net in base 128, because
- 1 times m-reduction [i] would yield (34, 76, 2889220)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 14059 153714 252336 960090 488402 264599 376338 325380 030482 215974 810392 777785 899616 755982 425160 254208 160878 599026 685055 332808 609426 144356 272411 622759 535195 582043 997568 > 12876 [i]