MinT - Best Known (102, 102+32, s)-Nets in Base 4

Best Known (102, 102+32, s)-Nets in Base 4

Digital (102, 134, 1032)-net over F₄, using

4² times duplication [i] based on digital (100, 132, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 33, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

Digital (102, 134, 1673)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹³⁴, 1673, F₄, 32) (dual of [1673, 1539, 33]-code), using
- 1538 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) [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 (102, 134, 249832)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 474 292700 364566 126892 374584 819795 206283 650847 926352 636217 150773 538081 947928 460946 > 4¹³⁴ [i]