Best Known (69−36, 69, s)-Nets in Base 128
(69−36, 69, 504)-Net over F128 — Constructive and digital
Digital (33, 69, 504)-net over F128, using
- 2 times m-reduction [i] based on digital (33, 71, 504)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (5, 24, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- digital (9, 47, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- digital (5, 24, 216)-net over F128, using
- (u, u+v)-construction [i] based on
(69−36, 69, 548)-Net in Base 128 — Constructive
(33, 69, 548)-net in base 128, using
- (u, u+v)-construction [i] based on
- (6, 24, 260)-net in base 128, using
- base change [i] based on digital (3, 21, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 21, 260)-net over F256, using
- digital (9, 45, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- (6, 24, 260)-net in base 128, using
(69−36, 69, 1580)-Net over F128 — Digital
Digital (33, 69, 1580)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12869, 1580, F128, 36) (dual of [1580, 1511, 37]-code), using
- 1418 step Varšamov–Edel lengthening with (ri) = (12, 0, 1, 0, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 11 times 0, 1, 15 times 0, 1, 21 times 0, 1, 26 times 0, 1, 31 times 0, 1, 37 times 0, 1, 42 times 0, 1, 48 times 0, 1, 56 times 0, 1, 65 times 0, 1, 74 times 0, 1, 86 times 0, 1, 100 times 0, 1, 114 times 0, 1, 131 times 0, 1, 151 times 0, 1, 174 times 0, 1, 201 times 0) [i] based on linear OA(12836, 129, F128, 36) (dual of [129, 93, 37]-code or 129-arc in PG(35,128)), using
- extended Reed–Solomon code RSe(93,128) [i]
- 1418 step Varšamov–Edel lengthening with (ri) = (12, 0, 1, 0, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 11 times 0, 1, 15 times 0, 1, 21 times 0, 1, 26 times 0, 1, 31 times 0, 1, 37 times 0, 1, 42 times 0, 1, 48 times 0, 1, 56 times 0, 1, 65 times 0, 1, 74 times 0, 1, 86 times 0, 1, 100 times 0, 1, 114 times 0, 1, 131 times 0, 1, 151 times 0, 1, 174 times 0, 1, 201 times 0) [i] based on linear OA(12836, 129, F128, 36) (dual of [129, 93, 37]-code or 129-arc in PG(35,128)), using
(69−36, 69, 7111546)-Net in Base 128 — Upper bound on s
There is no (33, 69, 7111547)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 24 974050 150997 498041 630158 672673 929750 631497 580707 420997 686777 827422 067546 126946 397677 363169 971406 984623 460798 446061 937303 892002 681007 681115 983881 > 12869 [i]