Best Known (72, 72+55, s)-Nets in Base 16
(72, 72+55, 530)-Net over F16 — Constructive and digital
Digital (72, 127, 530)-net over F16, using
- 1 times m-reduction [i] based on digital (72, 128, 530)-net over F16, using
- trace code for nets [i] based on digital (8, 64, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
- trace code for nets [i] based on digital (8, 64, 265)-net over F256, using
(72, 72+55, 1026)-Net over F16 — Digital
Digital (72, 127, 1026)-net over F16, using
- 1 times m-reduction [i] based on digital (72, 128, 1026)-net over F16, using
- trace code for nets [i] based on digital (8, 64, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- trace code for nets [i] based on digital (8, 64, 513)-net over F256, using
(72, 72+55, 303054)-Net in Base 16 — Upper bound on s
There is no (72, 127, 303055)-net in base 16, because
- 1 times m-reduction [i] would yield (72, 126, 303055)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 52 376090 778627 957749 734854 363449 400323 094000 082027 952003 534568 477655 312255 399792 603258 031109 281329 253361 986360 077556 470883 793524 330155 676054 260913 633776 > 16126 [i]