Best Known (128−98, 128, s)-Nets in Base 5
(128−98, 128, 51)-Net over F5 — Constructive and digital
Digital (30, 128, 51)-net over F5, using
- t-expansion [i] based on digital (22, 128, 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
(128−98, 128, 58)-Net over F5 — Digital
Digital (30, 128, 58)-net over F5, using
- net from sequence [i] based on digital (30, 57)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 30 and N(F) ≥ 58, using
(128−98, 128, 213)-Net over F5 — Upper bound on s (digital)
There is no digital (30, 128, 214)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(5128, 214, F5, 98) (dual of [214, 86, 99]-code), but
- construction Y1 [i] would yield
- OA(5127, 149, S5, 98), but
- the linear programming bound shows that M ≥ 5193 361256 119414 558729 044685 549653 156610 735015 094949 701472 602202 230455 237241 812938 009388 744831 085205 078125 / 69869 528585 224173 > 5127 [i]
- OA(586, 214, 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(5127, 149, S5, 98), but
- construction Y1 [i] would yield
(128−98, 128, 285)-Net in Base 5 — Upper bound on s
There is no (30, 128, 286)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 336430 116750 057100 477102 907192 097420 035041 777452 574825 976931 386263 125957 332363 663847 701625 > 5128 [i]