Best Known (148−133, 148, s)-Nets in Base 5
(148−133, 148, 36)-Net over F5 — Constructive and digital
Digital (15, 148, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-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 4 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]
(148−133, 148, 39)-Net over F5 — Digital
Digital (15, 148, 39)-net over F5, using
- t-expansion [i] based on digital (14, 148, 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
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(148−133, 148, 75)-Net in Base 5 — Upper bound on s
There is no (15, 148, 76)-net in base 5, because
- extracting embedded OOA [i] would yield OOA(5148, 76, S5, 2, 133), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2101 947696 487225 606385 594374 934874 196920 392912 814773 657635 602425 834686 624028 790902 229957 282543 182373 046875 / 67 > 5148 [i]