Best Known (202, 202+28, s)-Nets in Base 4
(202, 202+28, 74916)-Net over F4 — Constructive and digital
Digital (202, 230, 74916)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 19, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (183, 211, 74899)-net over F4, using
- net defined by OOA [i] based on linear OOA(4211, 74899, F4, 28, 28) (dual of [(74899, 28), 2096961, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(4211, 1048586, F4, 28) (dual of [1048586, 1048375, 29]-code), using
- 1 times truncation [i] based on linear OA(4212, 1048587, F4, 29) (dual of [1048587, 1048375, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4201, 1048576, F4, 27) (dual of [1048576, 1048375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(4212, 1048587, F4, 29) (dual of [1048587, 1048375, 30]-code), using
- OA 14-folding and stacking [i] based on linear OA(4211, 1048586, F4, 28) (dual of [1048586, 1048375, 29]-code), using
- net defined by OOA [i] based on linear OOA(4211, 74899, F4, 28, 28) (dual of [(74899, 28), 2096961, 29]-NRT-code), using
- digital (5, 19, 17)-net over F4, using
(202, 202+28, 706185)-Net over F4 — Digital
Digital (202, 230, 706185)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4230, 706185, F4, 28) (dual of [706185, 705955, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4230, 1048655, F4, 28) (dual of [1048655, 1048425, 29]-code), using
- 3 times code embedding in larger space [i] based on linear OA(4227, 1048652, F4, 28) (dual of [1048652, 1048425, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(416, 76, F4, 6) (dual of [76, 60, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 85, F4, 6) (dual of [85, 69, 7]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(4227, 1048652, F4, 28) (dual of [1048652, 1048425, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4230, 1048655, F4, 28) (dual of [1048655, 1048425, 29]-code), using
(202, 202+28, large)-Net in Base 4 — Upper bound on s
There is no (202, 230, large)-net in base 4, because
- 26 times m-reduction [i] would yield (202, 204, large)-net in base 4, but