Best Known (28, 28+∞, s)-Nets in Base 5
(28, 28+∞, 51)-Net over F5 — Constructive and digital
Digital (28, m, 51)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 50)-sequence over F5, using
- t-expansion [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
- t-expansion [i] based on digital (22, 50)-sequence over F5, using
(28, 28+∞, 55)-Net over F5 — Digital
Digital (28, m, 55)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (28, 54)-sequence over F5, using
- t-expansion [i] based on digital (23, 54)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 23 and N(F) ≥ 55, using
- t-expansion [i] based on digital (23, 54)-sequence over F5, using
(28, 28+∞, 127)-Net in Base 5 — Upper bound on s
There is no (28, m, 128)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (28, 380, 128)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5380, 128, S5, 3, 352), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18882 287269 628430 221158 742695 379243 988367 724241 776151 127149 088790 021706 632296 388086 057111 272175 035089 548704 557469 666665 098719 410787 780582 668688 455301 110777 551584 050758 033571 297606 981625 771733 922896 689034 225008 490222 288011 270283 282494 464316 414450 877346 098423 004150 390625 / 353 > 5380 [i]
- extracting embedded OOA [i] would yield OOA(5380, 128, S5, 3, 352), but