Best Known (138−105, 138, s)-Nets in Base 2
(138−105, 138, 24)-Net over F2 — Constructive and digital
Digital (33, 138, 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
(138−105, 138, 28)-Net over F2 — Digital
Digital (33, 138, 28)-net over F2, using
- net from sequence [i] based on digital (33, 27)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 28, using
(138−105, 138, 45)-Net in Base 2 — Upper bound on s
There is no (33, 138, 46)-net in base 2, because
- 7 times m-reduction [i] would yield (33, 131, 46)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2131, 46, S2, 3, 98), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 435561 429658 801233 233119 497512 663310 663680 / 99 > 2131 [i]
- extracting embedded OOA [i] would yield OOA(2131, 46, S2, 3, 98), but