MinT - Information on Result #1851780

Information on Result #1851780

There is no (80, m, 339)-net in base 5 for arbitrarily large m, because m-reduction would yield (80, 1351, 339)-net in base 5, but

extracting embedded OOA [i] would yield OOA(5¹³⁵¹, 339, S₅, 4, 1271), but
- the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 16276 680735 651404 463416 459269 625060 035726 102305 966419 016853 835060 468493 482238 436547 439924 592455 392327 669621 754736 375683 232303 239943 925672 377643 565447 580400 558813 395786 200073 219638 638863 932954 465461 027134 456178 164522 216530 012857 918182 644464 635330 384111 581880 806826 293880 647915 665233 335822 276248 263244 109147 897224 172034 966232 456178 865298 513707 555836 993581 777928 803574 300912 982751 504396 694139 877707 274410 891001 270895 473561 950928 034101 770966 372183 371985 418116 681096 184683 342146 449647 454376 175690 336745 100729 914097 372217 424854 947511 857032 410624 614094 573160 089119 941651 125894 422955 807917 149705 121997 682901 682424 181432 866824 468786 175402 172020 297033 647319 769614 036161 885599 504609 923455 811048 019523 675521 720227 822853 550747 296418 356727 314329 763530 589897 712539 466507 342853 932359 643849 188372 665594 613089 864518 983492 268355 051311 208345 906291 076488 949156 854269 850963 404244 086007 995306 320537 409649 937871 195839 875828 334855 634160 760473 605478 182435 035705 566406 250000 / 53 > 5¹³⁵¹ [i]

Mode: Bound.

Show details for fixed m and s, m and t, t and s.

None.

The following results depend on this result:

	Result		Method
1	No (80, 338)-sequence in base 5	[i]	Net from Sequence
2	No (80, 80+k, 339)-net in base 5 for arbitrarily large k	[i]	Logical Equivalence (for Nets with Unbounded m)
3	No (80, m, 339)-net in base 5 with unbounded m	[i]
4	No digital (80, 80+k, 339)-net over F₅ for arbitrarily large k	[i]
5	No digital (80, m, 339)-net over F₅ with unbounded m	[i]