Best Known (4, 4+∞, s)-Nets in Base 32
(4, 4+∞, 64)-Net over F32 — Constructive and digital
Digital (4, m, 64)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (4, 63)-sequence over F32, using
- t-expansion [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- t-expansion [i] based on digital (3, 63)-sequence over F32, using
(4, 4+∞, 71)-Net over F32 — Digital
Digital (4, m, 71)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (4, 70)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 4 and N(F) ≥ 71, using
(4, 4+∞, 165)-Net in Base 32 — Upper bound on s
There is no (4, m, 166)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (4, 164, 166)-net in base 32, but
- extracting embedded OOA [i] would yield OA(32164, 166, S32, 160), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1342 448621 178513 806457 130496 891008 054252 581523 695499 337317 567954 795831 125250 917382 469310 199960 529455 098251 226994 640611 878487 352847 987814 532833 360595 698339 669711 540983 186525 567293 756309 131827 130136 486250 385863 058475 434244 700315 824231 969943 145615 982592 / 161 > 32164 [i]
- extracting embedded OOA [i] would yield OA(32164, 166, S32, 160), but