Best Known (30, 132, s)-Nets in Base 5
(30, 132, 51)-Net over F5 — Constructive and digital
Digital (30, 132, 51)-net over F5, using
- t-expansion [i] based on digital (22, 132, 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
(30, 132, 58)-Net over F5 — Digital
Digital (30, 132, 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
(30, 132, 180)-Net over F5 — Upper bound on s (digital)
There is no digital (30, 132, 181)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(5132, 181, F5, 102) (dual of [181, 49, 103]-code), but
- construction Y1 [i] would yield
- OA(5131, 147, S5, 102), but
- the linear programming bound shows that M ≥ 249 236477 010921 693845 684281 987701 342304 847343 669838 056342 020625 628930 208250 721989 315934 479236 602783 203125 / 6 326951 585981 > 5131 [i]
- OA(549, 181, S5, 34), but
- discarding factors would yield OA(549, 179, S5, 34), but
- the linear programming bound shows that M ≥ 63101 461737 633561 195888 825311 804301 658299 627461 880998 569540 679454 803466 796875 / 3 393659 613629 526150 016067 267200 843099 664623 > 549 [i]
- discarding factors would yield OA(549, 179, S5, 34), but
- OA(5131, 147, S5, 102), but
- construction Y1 [i] would yield
(30, 132, 283)-Net in Base 5 — Upper bound on s
There is no (30, 132, 284)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 197 060313 469893 377004 738724 396420 808233 467567 986656 312065 432700 141226 554109 357854 233604 982385 > 5132 [i]