Best Known (193, ∞, s)-Nets in Base 2
(193, ∞, 66)-Net over F2 — Constructive and digital
Digital (193, m, 66)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (193, 65)-sequence over F2, using
- t-expansion [i] based on digital (163, 65)-sequence over F2, using
- base reduction for sequences [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- base reduction for sequences [i] based on digital (49, 65)-sequence over F4, using
- t-expansion [i] based on digital (163, 65)-sequence over F2, using
(193, ∞, 91)-Net over F2 — Digital
Digital (193, m, 91)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (193, 90)-sequence over F2, using
- t-expansion [i] based on digital (190, 90)-sequence over F2, using
- base reduction for sequences [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- base reduction for sequences [i] based on digital (50, 90)-sequence over F4, using
- t-expansion [i] based on digital (190, 90)-sequence over F2, using
(193, ∞, 203)-Net in Base 2 — Upper bound on s
There is no (193, m, 204)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (193, 1826, 204)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21826, 204, S2, 9, 1633), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 931750 356281 512516 390935 525188 786283 276513 527533 880228 881896 859845 881952 436176 470566 774539 807881 195760 287213 059959 261435 094760 984012 810371 484845 755649 708060 319142 044952 491819 634752 315671 428445 865147 306378 077034 736660 395237 607458 449045 972098 117517 698689 259084 449253 486558 632248 646562 449018 568628 140194 297122 368177 720064 083417 760551 072322 414799 553204 242036 167505 456920 381218 407869 004081 799000 254584 318039 368324 800340 902257 272828 234888 004703 188100 068349 016218 477443 774110 773418 379990 461685 758686 519605 240776 521160 522186 722050 236601 111305 789076 136242 708480 / 817 > 21826 [i]
- extracting embedded OOA [i] would yield OOA(21826, 204, S2, 9, 1633), but