Best Known (236−30, 236, s)-Nets in Base 4
(236−30, 236, 69910)-Net over F4 — Constructive and digital
Digital (206, 236, 69910)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 15, 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 (191, 221, 69905)-net over F4, using
- net defined by OOA [i] based on linear OOA(4221, 69905, F4, 30, 30) (dual of [(69905, 30), 2096929, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(4221, 1048575, F4, 30) (dual of [1048575, 1048354, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4221, 1048576, F4, 30) (dual of [1048576, 1048355, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(4221, 1048576, F4, 30) (dual of [1048576, 1048355, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(4221, 1048575, F4, 30) (dual of [1048575, 1048354, 31]-code), using
- net defined by OOA [i] based on linear OOA(4221, 69905, F4, 30, 30) (dual of [(69905, 30), 2096929, 31]-NRT-code), using
- digital (0, 15, 5)-net over F4, using
(236−30, 236, 524325)-Net over F4 — Digital
Digital (206, 236, 524325)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4236, 524325, F4, 2, 30) (dual of [(524325, 2), 1048414, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4236, 1048650, F4, 30) (dual of [1048650, 1048414, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4236, 1048651, F4, 30) (dual of [1048651, 1048415, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(21) [i] based on
- linear OA(4221, 1048576, F4, 30) (dual of [1048576, 1048355, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(415, 75, F4, 7) (dual of [75, 60, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(415, 85, F4, 7) (dual of [85, 70, 8]-code), using
- construction X applied to Ce(29) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(4236, 1048651, F4, 30) (dual of [1048651, 1048415, 31]-code), using
- OOA 2-folding [i] based on linear OA(4236, 1048650, F4, 30) (dual of [1048650, 1048414, 31]-code), using
(236−30, 236, large)-Net in Base 4 — Upper bound on s
There is no (206, 236, large)-net in base 4, because
- 28 times m-reduction [i] would yield (206, 208, large)-net in base 4, but