Best Known (44, 44+∞, s)-Nets in Base 9
(44, 44+∞, 81)-Net over F9 — Constructive and digital
Digital (44, m, 81)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (44, 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
(44, 44+∞, 147)-Net over F9 — Digital
Digital (44, m, 147)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (44, 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
(44, 44+∞, 377)-Net in Base 9 — Upper bound on s
There is no (44, m, 378)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (44, 1130, 378)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91130, 378, S9, 3, 1086), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 23 911782 094561 354290 233982 571928 091317 616852 923605 179870 940344 936820 714247 109015 159388 234141 194882 090901 459093 305991 040828 680046 002524 963012 192169 107376 686647 043066 730424 193685 273956 973587 823334 939215 817545 901389 845603 463632 790199 696236 888581 023809 523289 338780 676575 854107 136331 045046 050042 958662 409007 135618 389796 089187 755006 795594 295572 923361 914116 554672 726966 050034 426165 294661 276869 242966 561539 659937 137179 377979 832439 878030 425698 952153 030461 679421 092327 292561 645930 301450 329531 877586 211197 795852 264743 248530 512929 873863 741880 009137 539676 735868 131956 705554 937705 559918 345253 872457 330110 183410 147303 788383 443714 978653 706894 682468 878054 634277 313423 335924 911251 934011 150977 808735 991461 881353 583002 737819 808640 112893 435683 158830 469177 302881 726972 985365 399625 057514 084021 978434 997092 639731 895886 958680 481522 603059 918671 239808 819631 791759 325641 271791 951133 007200 353361 343440 516682 023895 758389 644589 895506 130286 197892 056663 749461 156599 598632 824509 046431 446616 577803 550168 688554 121570 445749 093734 895588 015243 372062 916376 546737 892935 170826 295454 891056 718678 608997 782444 499207 053251 399215 / 1087 > 91130 [i]
- extracting embedded OOA [i] would yield OOA(91130, 378, S9, 3, 1086), but