MinT - Best Known (91−33, 91, s)-Nets in Base 7

Best Known (91−33, 91, s)-Nets in Base 7

Digital (58, 91, 124)-net over F₇, using

1 times m-reduction [i] based on digital (58, 92, 124)-net over F₇, using
- trace code for nets [i] based on digital (12, 46, 62)-net over F₄₉, using
  - net from sequence [i] based on digital (12, 61)-sequence over F₄₉, using
    - Niederreiter sequence [i]

Digital (58, 91, 556)-net over F₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁹¹, 556, F₇, 33) (dual of [556, 465, 34]-code), using
- 464 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, 1, 26 times 0, 1, 28 times 0, 1, 30 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 (58, 91, 64269)-net in base 7, because

1 times m-reduction [i] would yield (58, 90, 64269)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 11453 129208 221028 306988 278112 707496 584826 582170 726840 957191 939364 145096 568065 > 7⁹⁰ [i]