Best Known (118, 118+22, s)-Nets in Base 4
(118, 118+22, 5963)-Net over F4 — Constructive and digital
Digital (118, 140, 5963)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 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 (107, 129, 5958)-net over F4, using
- net defined by OOA [i] based on linear OOA(4129, 5958, F4, 22, 22) (dual of [(5958, 22), 130947, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4129, 65538, F4, 22) (dual of [65538, 65409, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4129, 65544, F4, 22) (dual of [65544, 65415, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(40, 8, F4, 0) (dual of [8, 8, 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
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4129, 65544, F4, 22) (dual of [65544, 65415, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(4129, 65538, F4, 22) (dual of [65538, 65409, 23]-code), using
- net defined by OOA [i] based on linear OOA(4129, 5958, F4, 22, 22) (dual of [(5958, 22), 130947, 23]-NRT-code), using
- digital (0, 11, 5)-net over F4, using
(118, 118+22, 42300)-Net over F4 — Digital
Digital (118, 140, 42300)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4140, 42300, F4, 22) (dual of [42300, 42160, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4140, 65548, F4, 22) (dual of [65548, 65408, 23]-code), using
- (u, u+v)-construction [i] based on
- linear OA(411, 12, F4, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,4)), using
- dual of repetition code with length 12 [i]
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(411, 12, F4, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4140, 65548, F4, 22) (dual of [65548, 65408, 23]-code), using
(118, 118+22, large)-Net in Base 4 — Upper bound on s
There is no (118, 140, large)-net in base 4, because
- 20 times m-reduction [i] would yield (118, 120, large)-net in base 4, but