Best Known (30, 30+82, s)-Nets in Base 5
(30, 30+82, 51)-Net over F5 — Constructive and digital
Digital (30, 112, 51)-net over F5, using
- t-expansion [i] based on digital (22, 112, 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+82, 58)-Net over F5 — Digital
Digital (30, 112, 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+82, 296)-Net in Base 5 — Upper bound on s
There is no (30, 112, 297)-net in base 5, because
- 3 times m-reduction [i] would yield (30, 109, 297)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5109, 297, S5, 79), but
- 3 times code embedding in larger space [i] would yield OA(5112, 300, S5, 79), but
- the linear programming bound shows that M ≥ 60 123103 824233 614021 664937 889881 914446 607950 817463 333958 838758 443641 810008 771381 540946 109445 427412 509028 705981 397134 406332 013493 769997 528588 541359 102829 517175 021104 289458 546972 343967 324461 739096 490871 731364 978924 768163 101833 758531 427731 919954 234713 880900 980116 055994 053533 234526 880950 472071 103305 438913 473601 747483 598956 023342 907428 741455 078125 / 29 266961 190455 571613 939793 110953 847519 391373 884867 774883 035978 203069 533807 303542 026619 026592 815428 764885 668245 353719 642320 392847 980436 979375 894863 835262 271403 758345 189573 988251 353259 356016 075391 991560 522494 750453 905352 744614 862030 076521 395845 805850 415315 957654 775389 > 5112 [i]
- 3 times code embedding in larger space [i] would yield OA(5112, 300, S5, 79), but
- extracting embedded orthogonal array [i] would yield OA(5109, 297, S5, 79), but