Best Known (177−114, 177, s)-Nets in Base 3
(177−114, 177, 48)-Net over F3 — Constructive and digital
Digital (63, 177, 48)-net over F3, using
- t-expansion [i] based on digital (45, 177, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(177−114, 177, 64)-Net over F3 — Digital
Digital (63, 177, 64)-net over F3, using
- t-expansion [i] based on digital (49, 177, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(177−114, 177, 243)-Net over F3 — Upper bound on s (digital)
There is no digital (63, 177, 244)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(3177, 244, F3, 114) (dual of [244, 67, 115]-code), but
- residual code [i] would yield OA(363, 129, S3, 38), but
- the linear programming bound shows that M ≥ 27394 927246 658716 280505 609830 966754 266943 599771 852911 812347 362273 888033 481942 700619 226980 552002 566559 946056 337529 318911 460294 252528 636694 057168 840752 021056 474862 270473 251459 113635 843141 415069 511086 828824 930338 911632 126066 656289 807379 557563 / 23115 773756 594355 283863 169247 489965 804825 823732 470022 393460 320252 015985 427759 858337 716346 716301 916633 417720 028424 122936 248890 154114 809073 606419 796229 301212 883543 956929 715125 894881 086371 890183 753102 695045 896371 > 363 [i]
- residual code [i] would yield OA(363, 129, S3, 38), but
(177−114, 177, 281)-Net in Base 3 — Upper bound on s
There is no (63, 177, 282)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 937664 880535 540684 887906 411019 254944 191607 039566 929382 244731 775852 480457 986168 478085 > 3177 [i]