Best Known (238−36, 238, s)-Nets in Base 4
(238−36, 238, 3655)-Net over F4 — Constructive and digital
Digital (202, 238, 3655)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 22, 15)-net over F4, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 4 and N(F) ≥ 15, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- digital (180, 216, 3640)-net over F4, using
- net defined by OOA [i] based on linear OOA(4216, 3640, F4, 36, 36) (dual of [(3640, 36), 130824, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(4216, 65520, F4, 36) (dual of [65520, 65304, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4216, 65535, F4, 36) (dual of [65535, 65319, 37]-code), using
- 1 times truncation [i] based on linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 1 times truncation [i] based on linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4216, 65535, F4, 36) (dual of [65535, 65319, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(4216, 65520, F4, 36) (dual of [65520, 65304, 37]-code), using
- net defined by OOA [i] based on linear OOA(4216, 3640, F4, 36, 36) (dual of [(3640, 36), 130824, 37]-NRT-code), using
- digital (4, 22, 15)-net over F4, using
(238−36, 238, 65621)-Net over F4 — Digital
Digital (202, 238, 65621)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4238, 65621, F4, 36) (dual of [65621, 65383, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(25) [i] based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(421, 85, F4, 9) (dual of [85, 64, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 86, F4, 9) (dual of [86, 65, 10]-code), using
- construction X applied to Ce(36) ⊂ Ce(25) [i] based on
(238−36, 238, large)-Net in Base 4 — Upper bound on s
There is no (202, 238, large)-net in base 4, because
- 34 times m-reduction [i] would yield (202, 204, large)-net in base 4, but