MinT - Best Known (79, 102, s)-Nets in Base 4

Best Known (79, 102, s)-Nets in Base 4

Digital (79, 102, 1036)-net over F₄, using

4² times duplication [i] based on digital (77, 100, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 25, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

Digital (79, 102, 1878)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹⁰², 1878, F₄, 23) (dual of [1878, 1776, 24]-code), using
- 1775 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (6, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 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, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 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, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 33 times 0, 1, 34 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 49 times 0, 1, 51 times 0, 1, 55 times 0, 1, 59 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 76 times 0, 1, 81 times 0, 1, 87 times 0, 1, 92 times 0, 1, 99 times 0, 1, 105 times 0, 1, 112 times 0) [i] based on linear OA(4²³, 24, F₄, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
  - dual of repetition code with length 24 [i]

There is no (79, 102, 551940)-net in base 4, because

1 times m-reduction [i] would yield (79, 101, 551940)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 427819 274938 692875 918397 793786 842401 594505 303708 239331 035008 > 4¹⁰¹ [i]