Best Known (110, 130, s)-Nets in Base 3
(110, 130, 1977)-Net over F3 — Constructive and digital
Digital (110, 130, 1977)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 8)-net over F3, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- digital (98, 118, 1969)-net over F3, using
- net defined by OOA [i] based on linear OOA(3118, 1969, F3, 20, 20) (dual of [(1969, 20), 39262, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3118, 19690, F3, 20) (dual of [19690, 19572, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3118, 19692, F3, 20) (dual of [19692, 19574, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3109, 19683, F3, 19) (dual of [19683, 19574, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3118, 19692, F3, 20) (dual of [19692, 19574, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3118, 19690, F3, 20) (dual of [19690, 19572, 21]-code), using
- net defined by OOA [i] based on linear OOA(3118, 1969, F3, 20, 20) (dual of [(1969, 20), 39262, 21]-NRT-code), using
- digital (2, 12, 8)-net over F3, using
(110, 130, 9902)-Net over F3 — Digital
Digital (110, 130, 9902)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3130, 9902, F3, 20) (dual of [9902, 9772, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3130, 19731, F3, 20) (dual of [19731, 19601, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(382, 19683, F3, 14) (dual of [19683, 19601, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(312, 48, F3, 5) (dual of [48, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(312, 54, F3, 5) (dual of [54, 42, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(312, 54, F3, 5) (dual of [54, 42, 6]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3130, 19731, F3, 20) (dual of [19731, 19601, 21]-code), using
(110, 130, 3610118)-Net in Base 3 — Upper bound on s
There is no (110, 130, 3610119)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 106 111762 862610 066007 188866 363448 867732 517484 861562 197072 480637 > 3130 [i]