Best Known (24, 24+∞, s)-Nets in Base 8
(24, 24+∞, 65)-Net over F8 — Constructive and digital
Digital (24, m, 65)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (24, 64)-sequence over F8, using
- t-expansion [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- t-expansion [i] based on digital (14, 64)-sequence over F8, using
(24, 24+∞, 81)-Net over F8 — Digital
Digital (24, m, 81)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (24, 80)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 24 and N(F) ≥ 81, using
(24, 24+∞, 189)-Net in Base 8 — Upper bound on s
There is no (24, m, 190)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (24, 377, 190)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8377, 190, S8, 2, 353), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 367139 939634 256736 208896 848837 782732 429976 333996 346962 564446 045422 184178 581676 641086 951715 765508 084195 192045 814860 183984 842518 585837 674960 928623 918437 364161 603862 298370 568493 734455 160260 646633 877095 087735 222023 803812 823851 475429 792587 688597 087480 642061 982594 707945 133389 932479 403915 389849 090771 854813 867422 632459 117443 826656 675707 715669 983232 / 177 > 8377 [i]
- extracting embedded OOA [i] would yield OOA(8377, 190, S8, 2, 353), but