Best Known (98, 120, s)-Nets in Base 3
(98, 120, 688)-Net over F3 — Constructive and digital
Digital (98, 120, 688)-net over F3, using
- t-expansion [i] based on digital (97, 120, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 30, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 30, 172)-net over F81, using
(98, 120, 3294)-Net over F3 — Digital
Digital (98, 120, 3294)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3120, 3294, F3, 2, 22) (dual of [(3294, 2), 6468, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3120, 6588, F3, 22) (dual of [6588, 6468, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(3113, 6561, F3, 22) (dual of [6561, 6448, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(389, 6561, F3, 17) (dual of [6561, 6472, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(37, 27, F3, 4) (dual of [27, 20, 5]-code), using
- an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(3120, 6588, F3, 22) (dual of [6588, 6468, 23]-code), using
(98, 120, 393488)-Net in Base 3 — Upper bound on s
There is no (98, 120, 393489)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1797 050436 453129 021029 215782 266738 042157 167564 833432 558523 > 3120 [i]