Best Known (124−95, 124, s)-Nets in Base 5
(124−95, 124, 51)-Net over F5 — Constructive and digital
Digital (29, 124, 51)-net over F5, using
- t-expansion [i] based on digital (22, 124, 51)-net over F5, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
(124−95, 124, 56)-Net over F5 — Digital
Digital (29, 124, 56)-net over F5, using
- net from sequence [i] based on digital (29, 55)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 29 and N(F) ≥ 56, using
(124−95, 124, 209)-Net over F5 — Upper bound on s (digital)
There is no digital (29, 124, 210)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(5124, 210, F5, 95) (dual of [210, 86, 96]-code), but
- construction Y1 [i] would yield
- OA(5123, 145, S5, 95), but
- the linear programming bound shows that M ≥ 523946 922524 269524 545786 907827 294722 187715 168920 019132 326750 498085 399243 564097 560010 850429 534912 109375 / 4025 476446 595648 > 5123 [i]
- OA(586, 210, S5, 65), but
- discarding factors would yield OA(586, 145, S5, 65), but
- the linear programming bound shows that M ≥ 1 681971 586304 181223 187907 190141 264188 172812 749344 276629 843014 476462 881651 126808 966524 933987 666420 440086 867329 609762 499671 015636 681116 117777 216867 334999 506056 192331 016063 690185 546875 / 1 235197 506395 108210 300700 030853 409382 253498 637886 138574 180390 146599 149915 868081 543662 842688 306834 854616 250416 282850 014131 > 586 [i]
- discarding factors would yield OA(586, 145, S5, 65), but
- OA(5123, 145, S5, 95), but
- construction Y1 [i] would yield
(124−95, 124, 276)-Net in Base 5 — Upper bound on s
There is no (29, 124, 277)-net in base 5, because
- 1 times m-reduction [i] would yield (29, 123, 277)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 101 602272 954304 723630 806409 035219 158151 467971 289945 473724 680826 015922 071314 676159 284125 > 5123 [i]