Best Known (135, 135+11, s)-Nets in Base 2
(135, 135+11, 4194306)-Net over F2 — Constructive and digital
Digital (135, 146, 4194306)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 5)-net over F2, using
- net from sequence [i] based on digital (1, 4)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- nets constructed from net-embeddable BCH codes [i]
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (1, 4)-sequence over F2, using
- digital (129, 140, 4194301)-net over F2, using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2140, large, F2, 3, 11), using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- digital (1, 6, 5)-net over F2, using
(135, 135+11, 4770134)-Net over F2 — Digital
Digital (135, 146, 4770134)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2146, 4770134, F2, 3, 11) (dual of [(4770134, 3), 14310256, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2146, large, F2, 3, 11), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2140, large, F2, 3, 11), using
- discarding factors / shortening the dual code based on linear OOA(2146, large, F2, 3, 11), using
(135, 135+11, large)-Net in Base 2 — Upper bound on s
There is no (135, 146, large)-net in base 2, because
- 9 times m-reduction [i] would yield (135, 137, large)-net in base 2, but