Best Known (1, ∞, s)-Nets in Base 128
(1, ∞, 150)-Net over F128 — Constructive and digital
Digital (1, m, 150)-net over F128 for arbitrarily large m, using
- net from sequence [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
(1, ∞, 258)-Net in Base 128 — Upper bound on s
There is no (1, m, 259)-net in base 128 for arbitrarily large m, because
- m-reduction [i] would yield (1, 257, 259)-net in base 128, but
- extracting embedded OOA [i] would yield OA(128257, 259, S128, 256), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 13718 082926 732200 005197 300068 420734 463470 203798 109892 736581 116861 875633 911165 992703 903388 534433 834247 217947 842644 339985 155808 382443 728599 448848 977050 489477 042404 530844 871562 235418 478973 917013 654005 750701 641723 707489 829163 101036 229188 428176 663971 590526 008346 898785 754482 543639 143431 695318 286832 814589 457269 258155 512414 551072 298935 742746 873302 458157 903073 599864 815933 833638 232188 814456 573808 484849 409887 404680 222303 137787 111582 970857 229481 801247 364375 704147 356815 258261 439067 858184 222925 066687 490368 838103 607879 593973 113462 576877 551350 846368 776192 / 257 > 128257 [i]
- extracting embedded OOA [i] would yield OA(128257, 259, S128, 256), but