Best Known (191, 236, s)-Nets in Base 4
(191, 236, 1539)-Net over F4 — Constructive and digital
Digital (191, 236, 1539)-net over F4, using
- t-expansion [i] based on digital (190, 236, 1539)-net over F4, using
- 7 times m-reduction [i] based on digital (190, 243, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 81, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 81, 513)-net over F64, using
- 7 times m-reduction [i] based on digital (190, 243, 1539)-net over F4, using
(191, 236, 10947)-Net over F4 — Digital
Digital (191, 236, 10947)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4236, 10947, F4, 45) (dual of [10947, 10711, 46]-code), using
- discarding factors / shortening the dual code based on linear OA(4236, 16403, F4, 45) (dual of [16403, 16167, 46]-code), using
- construction XX applied to Ce(44) ⊂ Ce(41) ⊂ Ce(40) [i] based on
- linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4218, 16384, F4, 42) (dual of [16384, 16166, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(43, 18, F4, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(44) ⊂ Ce(41) ⊂ Ce(40) [i] based on
- discarding factors / shortening the dual code based on linear OA(4236, 16403, F4, 45) (dual of [16403, 16167, 46]-code), using
(191, 236, 8143782)-Net in Base 4 — Upper bound on s
There is no (191, 236, 8143783)-net in base 4, because
- 1 times m-reduction [i] would yield (191, 235, 8143783)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3048 584081 252521 181334 692971 089475 057431 577241 061464 775624 927389 822995 565542 071599 050813 000855 146259 964060 365552 390481 314405 293767 594355 273622 > 4235 [i]