MinT - Best Known (47−19, 47, s)-Nets in Base 7

Best Known (47−19, 47, s)-Nets in Base 7

Digital (28, 47, 108)-net over F₇, using

1 times m-reduction [i] based on digital (28, 48, 108)-net over F₇, using
- trace code for nets [i] based on digital (4, 24, 54)-net over F₄₉, using
  - net from sequence [i] based on digital (4, 53)-sequence over F₄₉, using
    - Niederreiter sequence [i]

Digital (28, 47, 212)-net over F₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁴⁷, 212, F₇, 19) (dual of [212, 165, 20]-code), using
- 164 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (4, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 13 times 0, 1, 15 times 0, 1, 17 times 0, 1, 19 times 0) [i] based on linear OA(7¹⁹, 20, F₇, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,7)), using
  - dual of repetition code with length 20 [i]

There is no (28, 47, 14416)-net in base 7, because

1 times m-reduction [i] would yield (28, 46, 14416)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 749 362463 730647 894539 647376 881049 769185 > 7⁴⁶ [i]