Best Known (74−51, 74, s)-Nets in Base 4
(74−51, 74, 34)-Net over F4 — Constructive and digital
Digital (23, 74, 34)-net over F4, using
- t-expansion [i] based on digital (21, 74, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(74−51, 74, 45)-Net over F4 — Digital
Digital (23, 74, 45)-net over F4, using
- net from sequence [i] based on digital (23, 44)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 23 and N(F) ≥ 45, using
(74−51, 74, 148)-Net in Base 4 — Upper bound on s
There is no (23, 74, 149)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(474, 149, S4, 51), but
- the linear programming bound shows that M ≥ 279 123203 196577 731183 924609 010058 174130 017835 652161 889854 733390 291715 322282 132144 255708 786599 657926 255286 680775 924735 427915 391859 785068 105496 087896 846613 696030 117599 875498 978225 995272 359016 687791 903500 078311 075896 698687 569123 571752 825442 897298 786867 689965 721234 282247 140616 543518 920686 145042 641597 285854 193756 874301 236317 639019 804676 074664 216793 750137 002551 825708 445515 357962 802175 612933 061176 897216 446464 / 763699 285149 072353 892250 053387 326736 742816 769207 104152 279331 909920 949243 302319 784056 272917 586529 212896 575800 771990 265507 229581 244962 600870 886555 748038 820436 666093 152832 805490 801146 159101 620949 588666 184504 191490 714280 313843 430672 252321 145347 356577 748776 537976 724579 824801 542772 367420 847363 935151 063757 571892 975638 892750 456084 589831 470914 117486 142320 702215 294985 > 474 [i]