Best Known (81, 81+∞, s)-Nets in Base 5
(81, 81+∞, 82)-Net over F5 — Constructive and digital
Digital (81, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (81, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(81, 81+∞, 150)-Net over F5 — Digital
Digital (81, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (81, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
(81, 81+∞, 342)-Net in Base 5 — Upper bound on s
There is no (81, m, 343)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (81, 1367, 343)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51367, 343, S5, 4, 1286), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 59451 758592 171553 702244 795801 795940 338927 242118 693718 752432 049066 156702 076886 379219 717894 734481 957068 419123 955383 604876 308175 477013 812375 265478 950180 275854 244475 656376 978187 972274 767731 536117 174831 136631 934320 802803 124723 386045 290603 187846 711459 513804 777720 918793 397486 573712 346881 557654 684096 191620 767628 141754 702466 889066 989102 415173 823833 407264 409464 082209 890069 553848 957002 889479 960017 902010 785096 848044 269113 219969 055227 633104 117203 908407 511428 977381 599996 936166 000767 614507 437000 992673 864110 694690 295212 684242 951578 568430 340227 253620 407087 531283 513383 270763 218093 528671 974489 863749 139071 584237 521824 469459 419191 089106 609144 514882 791174 763903 348562 010288 259359 457641 608081 585229 792380 978820 980522 691277 598726 411135 011926 282771 105119 857128 371263 653491 137629 090249 477331 534831 341960 304388 218982 416892 421531 530877 998318 501562 903359 103461 028913 048925 245528 077517 148993 690164 832076 322600 059572 910711 786744 192920 410741 719228 209234 415771 788917 481899 261474 609375 / 1287 > 51367 [i]
- extracting embedded OOA [i] would yield OOA(51367, 343, S5, 4, 1286), but