Best Known (140−127, 140, s)-Nets in Base 5
(140−127, 140, 34)-Net over F5 — Constructive and digital
Digital (13, 140, 34)-net over F5, using
- net from sequence [i] based on digital (13, 33)-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 2 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]
(140−127, 140, 36)-Net over F5 — Digital
Digital (13, 140, 36)-net over F5, using
- net from sequence [i] based on digital (13, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 13 and N(F) ≥ 36, using
(140−127, 140, 66)-Net in Base 5 — Upper bound on s
There is no (13, 140, 67)-net in base 5, because
- 9 times m-reduction [i] would yield (13, 131, 67)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5131, 67, S5, 2, 118), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4959 116792 531525 424243 107266 406348 953297 495317 632244 231365 046260 862072 813324 630260 467529 296875 / 119 > 5131 [i]
- extracting embedded OOA [i] would yield OOA(5131, 67, S5, 2, 118), but