Best Known (73−55, 73, s)-Nets in Base 128
(73−55, 73, 288)-Net over F128 — Constructive and digital
Digital (18, 73, 288)-net over F128, using
- t-expansion [i] based on digital (9, 73, 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
(73−55, 73, 386)-Net over F128 — Digital
Digital (18, 73, 386)-net over F128, using
- t-expansion [i] based on digital (15, 73, 386)-net over F128, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
(73−55, 73, 513)-Net in Base 128
(18, 73, 513)-net in base 128, using
- 1281 times duplication [i] based on (17, 72, 513)-net in base 128, using
- base change [i] based on digital (8, 63, 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
- base change [i] based on digital (8, 63, 513)-net over F256, using
(73−55, 73, 35782)-Net in Base 128 — Upper bound on s
There is no (18, 73, 35783)-net in base 128, because
- 1 times m-reduction [i] would yield (18, 72, 35783)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 52 398456 963770 717455 823356 017950 648167 241900 397378 854180 139153 740032 472679 525871 855650 188421 719843 304720 307476 633642 543136 026174 623417 570246 890114 521760 > 12872 [i]