Best Known (43, ∞, s)-Nets in Base 5
(43, ∞, 78)-Net over F5 — Constructive and digital
Digital (43, m, 78)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 77)-sequence over F5, using
- t-expansion [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- t-expansion [i] based on digital (38, 77)-sequence over F5, using
(43, ∞, 84)-Net over F5 — Digital
Digital (43, m, 84)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 83)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 43 and N(F) ≥ 84, using
(43, ∞, 188)-Net in Base 5 — Upper bound on s
There is no (43, m, 189)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (43, 563, 189)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5563, 189, S5, 3, 520), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 805131 909950 624746 793923 990096 830208 327361 771461 926024 330492 120560 896704 911974 842118 300850 332449 926241 917303 470798 950156 654932 547039 122936 445281 123297 806294 684025 699399 104003 866017 285273 673928 315524 671419 183204 056202 795409 822641 827987 008386 518733 080517 838825 373829 022495 354346 930352 545991 059529 238076 957538 704689 129246 165643 553885 715864 232880 996695 008069 159726 904473 473041 434772 312641 143798 828125 / 521 > 5563 [i]
- extracting embedded OOA [i] would yield OOA(5563, 189, S5, 3, 520), but