Best Known (11, 231, s)-Nets in Base 4
(11, 231, 27)-Net over F4 — Constructive and digital
Digital (11, 231, 27)-net over F4, using
- t-expansion [i] based on digital (10, 231, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
(11, 231, 44)-Net in Base 4 — Upper bound on s
There is no (11, 231, 45)-net in base 4, because
- 100 times m-reduction [i] would yield (11, 131, 45)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4131, 45, S4, 3, 120), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1452 495967 392894 355393 274435 948981 116111 418687 645795 235310 955933 795262 298203 357184 / 121 > 4131 [i]
- extracting embedded OOA [i] would yield OOA(4131, 45, S4, 3, 120), but