Best Known (126, 126+30, s)-Nets in Base 8
(126, 126+30, 2230)-Net over F8 — Constructive and digital
Digital (126, 156, 2230)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (10, 25, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- digital (101, 131, 2184)-net over F8, using
- net defined by OOA [i] based on linear OOA(8131, 2184, F8, 30, 30) (dual of [(2184, 30), 65389, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8131, 32760, F8, 30) (dual of [32760, 32629, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8131, 32760, F8, 30) (dual of [32760, 32629, 31]-code), using
- net defined by OOA [i] based on linear OOA(8131, 2184, F8, 30, 30) (dual of [(2184, 30), 65389, 31]-NRT-code), using
- digital (10, 25, 46)-net over F8, using
(126, 126+30, 4370)-Net in Base 8 — Constructive
(126, 156, 4370)-net in base 8, using
- base change [i] based on digital (87, 117, 4370)-net over F16, using
- 162 times duplication [i] based on digital (85, 115, 4370)-net over F16, using
- net defined by OOA [i] based on linear OOA(16115, 4370, F16, 30, 30) (dual of [(4370, 30), 130985, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(16115, 65550, F16, 30) (dual of [65550, 65435, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- linear OA(16113, 65536, F16, 30) (dual of [65536, 65423, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- OA 15-folding and stacking [i] based on linear OA(16115, 65550, F16, 30) (dual of [65550, 65435, 31]-code), using
- net defined by OOA [i] based on linear OOA(16115, 4370, F16, 30, 30) (dual of [(4370, 30), 130985, 31]-NRT-code), using
- 162 times duplication [i] based on digital (85, 115, 4370)-net over F16, using
(126, 126+30, 120248)-Net over F8 — Digital
Digital (126, 156, 120248)-net over F8, using
(126, 126+30, large)-Net in Base 8 — Upper bound on s
There is no (126, 156, large)-net in base 8, because
- 28 times m-reduction [i] would yield (126, 128, large)-net in base 8, but