Best Known (204, 204+36, s)-Nets in Base 4
(204, 204+36, 3658)-Net over F4 — Constructive and digital
Digital (204, 240, 3658)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 23, 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 (181, 217, 3641)-net over F4, using
- net defined by OOA [i] based on linear OOA(4217, 3641, F4, 36, 36) (dual of [(3641, 36), 130859, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(4217, 65538, F4, 36) (dual of [65538, 65321, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, 65544, F4, 36) (dual of [65544, 65327, 37]-code), using
- 1 times truncation [i] based on linear OA(4218, 65545, F4, 37) (dual of [65545, 65327, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [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(4209, 65536, F4, 35) (dual of [65536, 65327, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 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(36) ⊂ Ce(34) [i] based on
- 1 times truncation [i] based on linear OA(4218, 65545, F4, 37) (dual of [65545, 65327, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, 65544, F4, 36) (dual of [65544, 65327, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(4217, 65538, F4, 36) (dual of [65538, 65321, 37]-code), using
- net defined by OOA [i] based on linear OOA(4217, 3641, F4, 36, 36) (dual of [(3641, 36), 130859, 37]-NRT-code), using
- digital (5, 23, 17)-net over F4, using
(204, 204+36, 65625)-Net over F4 — Digital
Digital (204, 240, 65625)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4240, 65625, F4, 36) (dual of [65625, 65385, 37]-code), using
- construction X with 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
- linear OA(4238, 65623, F4, 35) (dual of [65623, 65385, 36]-code), using Gilbert–Varšamov bound and bm = 4238 > Vbs−1(k−1) = 3372 884204 626407 525351 638353 134438 610542 707573 581279 572274 227744 998520 741545 348659 911187 773635 745912 998980 600222 803902 733591 924562 389784 199332 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 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
- linear OA(4238, 65621, F4, 36) (dual of [65621, 65383, 37]-code), using
- construction X with Varšamov bound [i] based on
(204, 204+36, large)-Net in Base 4 — Upper bound on s
There is no (204, 240, large)-net in base 4, because
- 34 times m-reduction [i] would yield (204, 206, large)-net in base 4, but