Best Known (96, 114, s)-Nets in Base 4
(96, 114, 7287)-Net over F4 — Constructive and digital
Digital (96, 114, 7287)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (87, 105, 7282)-net over F4, using
- net defined by OOA [i] based on linear OOA(4105, 7282, F4, 18, 18) (dual of [(7282, 18), 130971, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(4105, 65538, F4, 18) (dual of [65538, 65433, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4105, 65544, F4, 18) (dual of [65544, 65439, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(40, 8, F4, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(4105, 65544, F4, 18) (dual of [65544, 65439, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(4105, 65538, F4, 18) (dual of [65538, 65433, 19]-code), using
- net defined by OOA [i] based on linear OOA(4105, 7282, F4, 18, 18) (dual of [(7282, 18), 130971, 19]-NRT-code), using
- digital (0, 9, 5)-net over F4, using
(96, 114, 40489)-Net over F4 — Digital
Digital (96, 114, 40489)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4114, 40489, F4, 18) (dual of [40489, 40375, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4114, 65546, F4, 18) (dual of [65546, 65432, 19]-code), using
- (u, u+v)-construction [i] based on
- linear OA(49, 10, F4, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,4)), using
- dual of repetition code with length 10 [i]
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(49, 10, F4, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4114, 65546, F4, 18) (dual of [65546, 65432, 19]-code), using
(96, 114, large)-Net in Base 4 — Upper bound on s
There is no (96, 114, large)-net in base 4, because
- 16 times m-reduction [i] would yield (96, 98, large)-net in base 4, but