Best Known (45, ∞, s)-Nets in Base 9
(45, ∞, 81)-Net over F9 — Constructive and digital
Digital (45, m, 81)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (45, 80)-sequence over F9, using
- t-expansion [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- t-expansion [i] based on digital (32, 80)-sequence over F9, using
(45, ∞, 147)-Net over F9 — Digital
Digital (45, m, 147)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (45, 146)-sequence over F9, using
- t-expansion [i] based on digital (43, 146)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 43 and N(F) ≥ 147, using
- t-expansion [i] based on digital (43, 146)-sequence over F9, using
(45, ∞, 385)-Net in Base 9 — Upper bound on s
There is no (45, m, 386)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (45, 1154, 386)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91154, 386, S9, 3, 1109), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 315538 204829 460019 723293 562566 793208 493362 831417 936215 392425 150297 069532 332842 232159 255715 095611 401943 534922 901427 085479 532025 374522 791533 596103 014455 862389 044219 017596 345915 889520 133248 746945 085415 736128 481719 110985 721452 827461 550217 562684 131170 754870 675196 109946 676411 659139 776754 388373 180649 975075 513392 661606 526893 683184 334265 130693 833874 098620 847276 327664 127295 976730 427120 423788 275527 384678 276153 817237 969882 484802 504073 078698 499981 210171 732943 335131 468956 123160 212278 919302 572567 578814 511493 765857 038804 227605 887038 490586 497493 447557 678136 438453 501464 403543 441062 772791 779979 219474 939522 341831 021966 465108 334483 069025 344287 397855 038127 705972 202548 780033 130957 845999 063477 511766 549563 277618 877402 034596 011809 376340 357583 212700 736727 243892 648936 083757 730088 526700 603643 422942 891074 743146 723228 595380 545848 051046 569872 331735 441052 404680 564731 807240 215258 466909 853565 475855 369085 871140 353150 898068 315120 034761 366850 053493 680836 656422 968732 896686 455284 475153 230382 754550 985565 209578 591496 083040 516218 712509 718960 992926 397081 632091 691673 674178 968426 607622 865220 756090 356170 098441 338653 099617 359838 884761 / 185 > 91154 [i]
- extracting embedded OOA [i] would yield OOA(91154, 386, S9, 3, 1109), but