MinT - Best Known (92−34, 92, s)-Nets in Base 7

Best Known (92−34, 92, s)-Nets in Base 7

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, 92, 515)-net over F₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁹², 515, F₇, 34) (dual of [515, 423, 35]-code), using
- 422 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (6, 3, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 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, 0, 0, 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, 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, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0) [i] based on linear OA(7³⁴, 35, F₇, 34) (dual of [35, 1, 35]-code or 35-arc in PG(33,7)), using
  - dual of repetition code with length 35 [i]

There is no (58, 92, 44788)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 561095 220889 780907 769554 215875 093419 148282 407228 534771 625421 563349 502138 280889 > 7⁹² [i]