Best Known (78−32, 78, s)-Nets in Base 25
(78−32, 78, 288)-Net over F25 — Constructive and digital
Digital (46, 78, 288)-net over F25, using
- t-expansion [i] based on digital (41, 78, 288)-net over F25, using
- net from sequence [i] based on digital (41, 287)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 41 and N(F) ≥ 288, using
- net from sequence [i] based on digital (41, 287)-sequence over F25, using
(78−32, 78, 1719)-Net over F25 — Digital
Digital (46, 78, 1719)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2578, 1719, F25, 32) (dual of [1719, 1641, 33]-code), using
- 1640 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 15 times 0, 1, 17 times 0, 1, 19 times 0, 1, 21 times 0, 1, 24 times 0, 1, 27 times 0, 1, 30 times 0, 1, 33 times 0, 1, 38 times 0, 1, 41 times 0, 1, 46 times 0, 1, 52 times 0, 1, 57 times 0, 1, 64 times 0, 1, 72 times 0, 1, 79 times 0, 1, 88 times 0, 1, 98 times 0, 1, 109 times 0, 1, 121 times 0, 1, 134 times 0, 1, 150 times 0, 1, 166 times 0) [i] based on linear OA(2532, 33, F25, 32) (dual of [33, 1, 33]-code or 33-arc in PG(31,25)), using
- dual of repetition code with length 33 [i]
- 1640 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 15 times 0, 1, 17 times 0, 1, 19 times 0, 1, 21 times 0, 1, 24 times 0, 1, 27 times 0, 1, 30 times 0, 1, 33 times 0, 1, 38 times 0, 1, 41 times 0, 1, 46 times 0, 1, 52 times 0, 1, 57 times 0, 1, 64 times 0, 1, 72 times 0, 1, 79 times 0, 1, 88 times 0, 1, 98 times 0, 1, 109 times 0, 1, 121 times 0, 1, 134 times 0, 1, 150 times 0, 1, 166 times 0) [i] based on linear OA(2532, 33, F25, 32) (dual of [33, 1, 33]-code or 33-arc in PG(31,25)), using
(78−32, 78, 1850474)-Net in Base 25 — Upper bound on s
There is no (46, 78, 1850475)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 10 947690 076359 133685 823802 118542 034112 850909 648786 592862 539023 049155 451158 260751 510620 972636 112797 836387 556481 > 2578 [i]