MinT - Best Known (55, 55+33, s)-Nets in Base 7

Best Known (55, 55+33, s)-Nets in Base 7

Digital (55, 88, 122)-net over F₇, using

trace code for nets [i] based on digital (11, 44, 61)-net over F₄₉, using
- net from sequence [i] based on digital (11, 60)-sequence over F₄₉, using
  - Niederreiter sequence [i]

Digital (55, 88, 466)-net over F₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁸⁸, 466, F₇, 33) (dual of [466, 378, 34]-code), using
- 377 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (6, 3, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 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, 9 times 0, 1, 9 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, 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) [i] based on linear OA(7³³, 34, F₇, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,7)), using
  - dual of repetition code with length 34 [i]

There is no (55, 88, 44618)-net in base 7, because

1 times m-reduction [i] would yield (55, 87, 44618)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 33 384512 196216 498813 959247 591992 068675 215245 041056 683834 505498 005581 245217 > 7⁸⁷ [i]