Best Known (132, 132+∞, s)-Nets in Base 2
(132, 132+∞, 57)-Net over F2 — Constructive and digital
Digital (132, m, 57)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (132, 56)-sequence over F2, using
- t-expansion [i] based on digital (110, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 8 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (110, 56)-sequence over F2, using
(132, 132+∞, 81)-Net over F2 — Digital
Digital (132, m, 81)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (132, 80)-sequence over F2, using
- t-expansion [i] based on digital (126, 80)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 126 and N(F) ≥ 81, using
- t-expansion [i] based on digital (126, 80)-sequence over F2, using
(132, 132+∞, 142)-Net in Base 2 — Upper bound on s
There is no (132, m, 143)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (132, 991, 143)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2991, 143, S2, 7, 859), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 729705 961408 133096 373907 443116 414241 931200 926668 956939 107179 448666 002686 606163 353192 633468 991157 498766 335860 925136 937158 052633 487626 229958 071317 445081 792784 549242 806856 008208 408521 212390 812261 844565 713215 993170 598221 716262 562737 242912 915882 448078 552134 942195 228825 253693 861605 377916 233252 360314 421248 / 215 > 2991 [i]
- extracting embedded OOA [i] would yield OOA(2991, 143, S2, 7, 859), but