Best Known (202, 202+39, s)-Nets in Base 4
(202, 202+39, 3451)-Net over F4 — Constructive and digital
Digital (202, 241, 3451)-net over F4, using
- 41 times duplication [i] based on digital (201, 240, 3451)-net over F4, using
- net defined by OOA [i] based on linear OOA(4240, 3451, F4, 39, 39) (dual of [(3451, 39), 134349, 40]-NRT-code), using
- OOA 19-folding and stacking with additional row [i] based on linear OA(4240, 65570, F4, 39) (dual of [65570, 65330, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(4240, 65575, F4, 39) (dual of [65575, 65335, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(33) [i] based on
- linear OA(4233, 65536, F4, 39) (dual of [65536, 65303, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(38) ⊂ Ce(33) [i] based on
- discarding factors / shortening the dual code based on linear OA(4240, 65575, F4, 39) (dual of [65575, 65335, 40]-code), using
- OOA 19-folding and stacking with additional row [i] based on linear OA(4240, 65570, F4, 39) (dual of [65570, 65330, 40]-code), using
- net defined by OOA [i] based on linear OOA(4240, 3451, F4, 39, 39) (dual of [(3451, 39), 134349, 40]-NRT-code), using
(202, 202+39, 39239)-Net over F4 — Digital
Digital (202, 241, 39239)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4241, 39239, F4, 39) (dual of [39239, 38998, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(4241, 65576, F4, 39) (dual of [65576, 65335, 40]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4240, 65575, F4, 39) (dual of [65575, 65335, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(33) [i] based on
- linear OA(4233, 65536, F4, 39) (dual of [65536, 65303, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(38) ⊂ Ce(33) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4240, 65575, F4, 39) (dual of [65575, 65335, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(4241, 65576, F4, 39) (dual of [65576, 65335, 40]-code), using
(202, 202+39, large)-Net in Base 4 — Upper bound on s
There is no (202, 241, large)-net in base 4, because
- 37 times m-reduction [i] would yield (202, 204, large)-net in base 4, but