Best Known (102−11, 102, s)-Nets in Base 4
(102−11, 102, 1677725)-Net over F4 — Constructive and digital
Digital (91, 102, 1677725)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- a shift-net [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (86, 97, 1677720)-net over F4, using
- net defined by OOA [i] based on linear OOA(497, 1677720, F4, 11, 11) (dual of [(1677720, 11), 18454823, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(497, 8388601, F4, 11) (dual of [8388601, 8388504, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(497, 8388601, F4, 11) (dual of [8388601, 8388504, 12]-code), using
- net defined by OOA [i] based on linear OOA(497, 1677720, F4, 11, 11) (dual of [(1677720, 11), 18454823, 12]-NRT-code), using
- digital (0, 5, 5)-net over F4, using
(102−11, 102, 7890070)-Net over F4 — Digital
Digital (91, 102, 7890070)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4102, 7890070, F4, 11) (dual of [7890070, 7889968, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4102, large, F4, 11) (dual of [large, large−102, 12]-code), using
- 5 times code embedding in larger space [i] based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- 5 times code embedding in larger space [i] based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4102, large, F4, 11) (dual of [large, large−102, 12]-code), using
(102−11, 102, large)-Net in Base 4 — Upper bound on s
There is no (91, 102, large)-net in base 4, because
- 9 times m-reduction [i] would yield (91, 93, large)-net in base 4, but