Best Known (2, ∞, s)-Nets in Base 128
(2, ∞, 150)-Net over F128 — Constructive and digital
Digital (2, m, 150)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (2, 149)-sequence over F128, using
- t-expansion [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- t-expansion [i] based on digital (1, 149)-sequence over F128, using
(2, ∞, 172)-Net over F128 — Digital
Digital (2, m, 172)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (2, 171)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 2 and N(F) ≥ 172, using
(2, ∞, 387)-Net in Base 128 — Upper bound on s
There is no (2, m, 388)-net in base 128 for arbitrarily large m, because
- m-reduction [i] would yield (2, 386, 388)-net in base 128, but
- extracting embedded OOA [i] would yield OA(128386, 388, S128, 384), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 236853 450727 792992 269799 335221 018419 882904 331695 476092 503226 000656 869252 919907 712877 188861 314805 468352 428175 508246 139420 805429 067735 850799 004416 986489 038813 044331 422584 496076 228250 787131 690815 217893 714403 267414 966384 650480 642322 052515 791013 426741 728346 796039 631332 533878 165469 174960 670257 347133 160296 728775 101800 593622 275503 967161 878968 949985 291022 616679 189808 442000 724024 667125 068976 638819 066420 926511 095819 399098 975333 967620 339655 395056 745898 354282 626564 275458 223067 352387 695901 371839 821768 398200 419610 688072 164856 415124 771557 677771 173546 521740 143722 799050 843634 310678 925794 178819 821312 996568 736509 691400 612156 723045 684504 715551 284781 700488 274656 459601 237049 340340 125756 863225 483525 952281 398080 543307 093087 195352 083476 545421 280053 145621 057979 191271 071768 480785 332507 827092 946601 583488 855880 915874 466593 459612 418048 / 385 > 128386 [i]
- extracting embedded OOA [i] would yield OA(128386, 388, S128, 384), but