Best Known (51, 51+65, s)-Nets in Base 3
(51, 51+65, 48)-Net over F3 — Constructive and digital
Digital (51, 116, 48)-net over F3, using
- t-expansion [i] based on digital (45, 116, 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
(51, 51+65, 64)-Net over F3 — Digital
Digital (51, 116, 64)-net over F3, using
- t-expansion [i] based on digital (49, 116, 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
(51, 51+65, 298)-Net in Base 3 — Upper bound on s
There is no (51, 116, 299)-net in base 3, because
- 1 times m-reduction [i] would yield (51, 115, 299)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3115, 299, S3, 64), but
- 1 times code embedding in larger space [i] would yield OA(3116, 300, S3, 64), but
- the linear programming bound shows that M ≥ 2428 161854 425644 193575 248457 855181 776168 527408 097863 807634 233217 823876 165815 693795 745216 765145 877578 680500 308634 974775 879629 518938 687498 980499 256760 399744 851190 654725 295306 338181 061636 563364 964130 843101 427006 831144 762461 688432 899855 134803 802305 025523 125150 720000 / 100 368157 007646 462287 720615 013336 709854 911951 718623 855583 358593 891344 806353 386207 853326 673779 884530 889009 112071 292241 469692 100586 866232 818423 278320 039802 894560 842727 757114 975109 361231 667182 655789 598323 441353 > 3116 [i]
- 1 times code embedding in larger space [i] would yield OA(3116, 300, S3, 64), but
- extracting embedded orthogonal array [i] would yield OA(3115, 299, S3, 64), but