Best Known (147−133, 147, s)-Nets in Base 5
(147−133, 147, 35)-Net over F5 — Constructive and digital
Digital (14, 147, 35)-net over F5, using
- net from sequence [i] based on digital (14, 34)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 3 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(147−133, 147, 39)-Net over F5 — Digital
Digital (14, 147, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
(147−133, 147, 70)-Net in Base 5 — Upper bound on s
There is no (14, 147, 71)-net in base 5, because
- 8 times m-reduction [i] would yield (14, 139, 71)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5139, 71, S5, 2, 125), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 932 704257 854598 242406 834410 637768 176980 142348 513008 897681 504649 757044 944635 708816 349506 378173 828125 / 63 > 5139 [i]
- extracting embedded OOA [i] would yield OOA(5139, 71, S5, 2, 125), but