Best Known (49, ∞, s)-Nets in Base 5
(49, ∞, 82)-Net over F5 — Constructive and digital
Digital (49, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (49, 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
(49, ∞, 96)-Net over F5 — Digital
Digital (49, m, 96)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (49, 95)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 49 and N(F) ≥ 96, using
(49, ∞, 213)-Net in Base 5 — Upper bound on s
There is no (49, m, 214)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (49, 638, 214)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5638, 214, S5, 3, 589), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5874 049055 342520 146537 217527 138203 831450 567375 292418 150370 580350 486847 533525 633098 574714 205664 088159 631392 152588 175607 331383 144191 733231 890281 689687 926686 499955 946051 006200 829499 193769 207812 454634 371932 351828 420594 543288 671792 324595 333199 182784 035211 224341 343827 968843 185903 414952 964579 798837 639549 359048 793149 075098 244725 975197 362320 863386 828203 567417 160778 627086 654307 659781 937583 466994 350378 710582 590078 941034 317239 200390 758924 186229 705810 546875 / 59 > 5638 [i]
- extracting embedded OOA [i] would yield OOA(5638, 214, S5, 3, 589), but