Best Known (131−88, 131, s)-Nets in Base 2
(131−88, 131, 33)-Net over F2 — Constructive and digital
Digital (43, 131, 33)-net over F2, using
- t-expansion [i] based on digital (39, 131, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
(131−88, 131, 34)-Net over F2 — Digital
Digital (43, 131, 34)-net over F2, using
- net from sequence [i] based on digital (43, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 43 and N(F) ≥ 34, using
(131−88, 131, 65)-Net in Base 2 — Upper bound on s
There is no (43, 131, 66)-net in base 2, because
- 5 times m-reduction [i] would yield (43, 126, 66)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2126, 66, S2, 2, 83), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 680 564733 841876 926926 749214 863536 422912 / 7 > 2126 [i]
- extracting embedded OOA [i] would yield OOA(2126, 66, S2, 2, 83), but