Best Known (108, 108+83, s)-Nets in Base 2
(108, 108+83, 57)-Net over F2 — Constructive and digital
Digital (108, 191, 57)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (13, 54, 15)-net over F2, using
- net from sequence [i] based on digital (13, 14)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 13 and N(F) ≥ 15, using
- net from sequence [i] based on digital (13, 14)-sequence over F2, using
- digital (54, 137, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- digital (13, 54, 15)-net over F2, using
(108, 108+83, 73)-Net over F2 — Digital
Digital (108, 191, 73)-net over F2, using
(108, 108+83, 296)-Net in Base 2 — Upper bound on s
There is no (108, 191, 297)-net in base 2, because
- 1 times m-reduction [i] would yield (108, 190, 297)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2190, 297, S2, 82), but
- 2 times code embedding in larger space [i] would yield OA(2192, 299, S2, 82), but
- adding a parity check bit [i] would yield OA(2193, 300, S2, 83), but
- the linear programming bound shows that M ≥ 47301 037877 562348 126535 964476 521603 387556 508620 623293 070152 196591 060102 430290 310541 234357 121691 993687 546336 928736 477184 / 2 739614 630568 907331 852802 953012 407724 450650 903550 704398 106875 > 2193 [i]
- adding a parity check bit [i] would yield OA(2193, 300, S2, 83), but
- 2 times code embedding in larger space [i] would yield OA(2192, 299, S2, 82), but
- extracting embedded orthogonal array [i] would yield OA(2190, 297, S2, 82), but