MinT - Best Known (120−28, 120, s)-Nets in Base 4

Best Known (120−28, 120, s)-Nets in Base 4

Digital (92, 120, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 30, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

Digital (92, 120, 1740)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹²⁰, 1740, F₄, 28) (dual of [1740, 1620, 29]-code), using
- 1619 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (8, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 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, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 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, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 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, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 53 times 0, 1, 55 times 0, 1, 58 times 0, 1, 62 times 0, 1, 65 times 0, 1, 68 times 0, 1, 72 times 0, 1, 76 times 0, 1, 80 times 0, 1, 85 times 0) [i] based on linear OA(4²⁸, 29, F₄, 28) (dual of [29, 1, 29]-code or 29-arc in PG(27,4)), using
  - dual of repetition code with length 29 [i]

There is no (92, 120, 291632)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 766910 220427 747637 090216 146572 840742 676733 633931 800134 391052 043939 998635 > 4¹²⁰ [i]