Best Known (93, 110, s)-Nets in Base 3
(93, 110, 2469)-Net over F3 — Constructive and digital
Digital (93, 110, 2469)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 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 (83, 100, 2461)-net over F3, using
- net defined by OOA [i] based on linear OOA(3100, 2461, F3, 17, 17) (dual of [(2461, 17), 41737, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3100, 19689, F3, 17) (dual of [19689, 19589, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3100, 19692, F3, 17) (dual of [19692, 19592, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3100, 19683, F3, 17) (dual of [19683, 19583, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(16) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3100, 19692, F3, 17) (dual of [19692, 19592, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3100, 19689, F3, 17) (dual of [19689, 19589, 18]-code), using
- net defined by OOA [i] based on linear OOA(3100, 2461, F3, 17, 17) (dual of [(2461, 17), 41737, 18]-NRT-code), using
- digital (2, 10, 8)-net over F3, using
(93, 110, 9861)-Net over F3 — Digital
Digital (93, 110, 9861)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3110, 9861, F3, 2, 17) (dual of [(9861, 2), 19612, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3110, 19722, F3, 17) (dual of [19722, 19612, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(3100, 19683, F3, 17) (dual of [19683, 19583, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(364, 19683, F3, 11) (dual of [19683, 19619, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(310, 39, F3, 5) (dual of [39, 29, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(3110, 19722, F3, 17) (dual of [19722, 19612, 18]-code), using
(93, 110, 5962612)-Net in Base 3 — Upper bound on s
There is no (93, 110, 5962613)-net in base 3, because
- 1 times m-reduction [i] would yield (93, 109, 5962613)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 10144 176408 562779 349566 374385 894766 129896 593633 888097 > 3109 [i]