Best Known (64−34, 64, s)-Nets in Base 128
(64−34, 64, 480)-Net over F128 — Constructive and digital
Digital (30, 64, 480)-net over F128, using
- 2 times m-reduction [i] based on digital (30, 66, 480)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 21, 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, 45, 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, 21, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(64−34, 64, 546)-Net in Base 128 — Constructive
(30, 64, 546)-net in base 128, using
- (u, u+v)-construction [i] based on
- (4, 21, 258)-net in base 128, using
- 3 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
- 3 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- digital (9, 43, 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, 21, 258)-net in base 128, using
(64−34, 64, 1282)-Net over F128 — Digital
Digital (30, 64, 1282)-net over F128, using
(64−34, 64, 4843580)-Net in Base 128 — Upper bound on s
There is no (30, 64, 4843581)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 726 839928 361653 137339 264247 540813 126412 584488 595160 509261 278158 876871 607533 195363 153523 011718 134731 995313 753417 728163 943586 572966 802884 > 12864 [i]