Best Known (115−79, 115, s)-Nets in Base 2
(115−79, 115, 24)-Net over F2 — Constructive and digital
Digital (36, 115, 24)-net over F2, using
- t-expansion [i] based on digital (33, 115, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
(115−79, 115, 30)-Net over F2 — Digital
Digital (36, 115, 30)-net over F2, using
- net from sequence [i] based on digital (36, 29)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 36 and N(F) ≥ 30, using
(115−79, 115, 56)-Net in Base 2 — Upper bound on s
There is no (36, 115, 57)-net in base 2, because
- 8 times m-reduction [i] would yield (36, 107, 57)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2107, 57, S2, 2, 71), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 649 037107 316853 453566 312041 152512 / 3 > 2107 [i]
- extracting embedded OOA [i] would yield OOA(2107, 57, S2, 2, 71), but