Best Known (109−88, 109, s)-Nets in Base 7
(109−88, 109, 29)-Net over F7 — Constructive and digital
Digital (21, 109, 29)-net over F7, using
- net from sequence [i] based on digital (21, 28)-sequence over F7, using
(109−88, 109, 64)-Net over F7 — Digital
Digital (21, 109, 64)-net over F7, using
- net from sequence [i] based on digital (21, 63)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 21 and N(F) ≥ 64, using
(109−88, 109, 297)-Net in Base 7 — Upper bound on s
There is no (21, 109, 298)-net in base 7, because
- 5 times m-reduction [i] would yield (21, 104, 298)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7104, 298, S7, 83), but
- 2 times code embedding in larger space [i] would yield OA(7106, 300, S7, 83), but
- the linear programming bound shows that M ≥ 2433 587325 685971 642123 011675 293819 324509 520288 080924 839071 509710 493320 438233 776369 213043 386155 823402 232653 749555 336133 563433 957151 423116 382708 286358 316295 761216 955295 388971 335377 113140 692145 954899 954239 261514 140006 426412 832202 239802 879774 203340 824805 592559 550696 862897 157668 584295 545849 551946 718293 282158 771465 272079 056185 360990 727033 126950 / 5843 066378 688195 853236 107487 744495 885852 722398 154587 816654 161346 609358 359487 180080 344955 941382 539833 164516 075668 605345 706572 942051 821286 337534 880581 268719 795760 182528 702016 851279 201492 990134 983780 029853 283363 853708 675665 299799 569186 129147 596841 576549 > 7106 [i]
- 2 times code embedding in larger space [i] would yield OA(7106, 300, S7, 83), but
- extracting embedded orthogonal array [i] would yield OA(7104, 298, S7, 83), but