Best Known (78, 78+∞, s)-Nets in Base 5
(78, 78+∞, 82)-Net over F5 — Constructive and digital
Digital (78, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (78, 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
(78, 78+∞, 150)-Net over F5 — Digital
Digital (78, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (78, 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
(78, 78+∞, 330)-Net in Base 5 — Upper bound on s
There is no (78, m, 331)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (78, 1319, 331)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51319, 331, S5, 4, 1241), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8 432629 755801 130413 362830 844558 153783 654799 247757 162114 289125 636624 899909 567766 047604 466455 822058 380334 209922 844745 790989 445507 099126 447428 962754 564027 081616 888716 423379 793662 557876 324812 187649 751105 443297 606770 388774 937583 946658 181997 896230 003315 763419 939517 535863 733538 544336 899655 926357 949144 790361 123369 056226 686047 214509 174401 287260 369195 303375 249221 709005 607393 658233 440555 019606 310918 058263 331138 988574 427353 529700 806319 762574 408747 757978 706830 041378 765933 566593 007844 423698 227586 279755 301801 813486 817488 053401 312121 288558 717250 768899 231550 492572 995950 499319 808698 869618 390550 788237 349738 426467 092675 493731 595068 152609 287915 597241 629681 351657 280926 370354 363895 106944 086622 467633 170358 051035 184011 899549 624014 433819 496893 869247 236872 713443 015655 017097 941243 291503 514623 138769 526573 168528 207683 899998 809739 757451 287771 616688 285060 955550 313504 271497 973116 976318 718617 165363 528168 954554 420366 775957 518257 200717 926025 390625 / 621 > 51319 [i]
- extracting embedded OOA [i] would yield OOA(51319, 331, S5, 4, 1241), but