Best Known (28, 28+∞, s)-Nets in Base 8
(28, 28+∞, 65)-Net over F8 — Constructive and digital
Digital (28, m, 65)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 64)-sequence over F8, using
- t-expansion [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- t-expansion [i] based on digital (14, 64)-sequence over F8, using
(28, 28+∞, 97)-Net over F8 — Digital
Digital (28, m, 97)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
(28, 28+∞, 218)-Net in Base 8 — Upper bound on s
There is no (28, m, 219)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (28, 653, 219)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8653, 219, S8, 3, 625), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 24017 032038 780465 934319 330360 346326 081083 413690 103033 887667 864243 660573 276451 502550 756384 321429 908785 034292 292672 682054 934997 482723 565801 846049 381485 348042 828263 621689 458727 269228 274239 226457 503199 210994 093484 110908 113104 086323 186227 566944 571033 001387 430112 307244 918816 702251 942200 165721 618139 078648 870524 111006 351692 072217 964366 501751 847166 403617 846840 551165 428080 388611 324507 901749 115896 659615 476130 927634 375385 583706 897713 789142 407855 948688 072980 443912 272204 344597 085119 153802 742409 260508 938882 625474 195718 092466 434947 273429 203477 801399 504199 644336 953306 583538 164149 334840 920466 426146 324480 / 313 > 8653 [i]
- extracting embedded OOA [i] would yield OOA(8653, 219, S8, 3, 625), but