MinT - Best Known (108, 140, s)-Nets in Base 4

Best Known (108, 140, s)-Nets in Base 4

Digital (108, 140, 1040)-net over F₄, using

trace code for nets [i] based on digital (3, 35, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

Digital (108, 140, 2183)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹⁴⁰, 2183, F₄, 32) (dual of [2183, 2043, 33]-code), using
- 2042 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (9, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 40 times 0, 1, 43 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 58 times 0, 1, 61 times 0, 1, 65 times 0, 1, 67 times 0, 1, 71 times 0, 1, 73 times 0, 1, 77 times 0, 1, 81 times 0, 1, 85 times 0, 1, 89 times 0, 1, 93 times 0) [i] based on linear OA(4³², 33, F₄, 32) (dual of [33, 1, 33]-code or 33-arc in PG(31,4)), using
  - dual of repetition code with length 33 [i]

There is no (108, 140, 420174)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 942672 140172 655815 828262 340116 644695 049081 249930 104386 515177 186123 934025 688602 067348 > 4¹⁴⁰ [i]