Best Known (38, ∞, s)-Nets in Base 5
(38, ∞, 78)-Net over F5 — Constructive and digital
Digital (38, m, 78)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
(38, ∞, 168)-Net in Base 5 — Upper bound on s
There is no (38, m, 169)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (38, 503, 169)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5503, 169, S5, 3, 465), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 088321 079496 734167 981017 658832 351305 549974 726328 891374 012099 955181 460141 949431 663056 286640 007230 425066 511773 147091 603924 081985 283655 276164 218141 171934 076998 180945 574815 156578 604100 178516 958233 568415 881212 950126 442569 242582 665074 958955 023741 212630 262556 060494 996799 903422 005108 032464 506452 024847 198371 103885 509666 477082 735269 732438 609935 343265 533447 265625 / 233 > 5503 [i]
- extracting embedded OOA [i] would yield OOA(5503, 169, S5, 3, 465), but