Best Known (30, 30+100, s)-Nets in Base 5
(30, 30+100, 51)-Net over F5 — Constructive and digital
Digital (30, 130, 51)-net over F5, using
- t-expansion [i] based on digital (22, 130, 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, 30+100, 58)-Net over F5 — Digital
Digital (30, 130, 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, 30+100, 191)-Net over F5 — Upper bound on s (digital)
There is no digital (30, 130, 192)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(5130, 192, F5, 100) (dual of [192, 62, 101]-code), but
- construction Y1 [i] would yield
- OA(5129, 148, S5, 100), but
- the linear programming bound shows that M ≥ 437019 493054 884386 993159 269280 163944 474914 010322 994172 449412 913421 078197 284685 984413 954429 328441 619873 046875 / 236583 689197 696731 > 5129 [i]
- OA(562, 192, S5, 44), but
- discarding factors would yield OA(562, 190, S5, 44), but
- the linear programming bound shows that M ≥ 5 531619 630605 621733 791634 558919 444104 118885 526484 067787 791939 510637 894272 804260 253906 250000 000000 000000 / 236416 842360 352611 941840 260955 732881 660879 805306 461094 587839 > 562 [i]
- discarding factors would yield OA(562, 190, S5, 44), but
- OA(5129, 148, S5, 100), but
- construction Y1 [i] would yield
(30, 30+100, 284)-Net in Base 5 — Upper bound on s
There is no (30, 130, 285)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 8 232151 378498 065941 569974 312281 968429 931138 562286 792790 136512 002558 506638 633473 253837 622105 > 5130 [i]